Version A Worksheet Function Frontiers
Domain & Range Practice • Version A
Name:
Date:
Instructions: For each function provided, identify the correct domain or range from the given options. Consider the characteristics of quadratic, square root, and exponential functions. Show any scratch work in the spaces provided.
1
What is the domain of the function \( f(x) = x^2 - 4x + 7 \)?
A) \( (-\infty, \infty) \)
B) \( [3, \infty) \)
C) \( [0, \infty) \)
D) \( (-\infty, 3] \)
2
What is the range of the function \( g(x) = \sqrt{x+5} - 2 \)?
A) \( [-5, \infty) \)
B) \( [-2, \infty) \)
C) \( (2, \infty) \)
D) \( (-\infty, \infty) \)
3
What is the range of the function \( h(x) = 3^x + 1 \)?
A) \( [1, \infty) \)
B) \( (-\infty, \infty) \)
C) \( (1, \infty) \)
D) \( (0, \infty) \)
4
What is the range of the function \( f(x) = -2(x-3)^2 + 5 \)?
A) \( [5, \infty) \)
B) \( (-\infty, 5] \)
C) \( (-\infty, \infty) \)
D) \( [-2, 5] \)
5
What is the domain of the function \( j(x) = \sqrt{8-2x} \)?
A) \( [4, \infty) \)
B) \( (-\infty, 4] \)
C) \( [0, \infty) \)
D) \( (-\infty, \infty) \)
6
What is the domain of the function \( k(x) = 0.5^{x+2} - 10 \)?
A) \( (-10, \infty) \)
B) \( (-\infty, \infty) \)
C) \( [-2, \infty) \)
D) \( x \neq -2 \)
7
Find the range of \( f(x) = x^2 + 6x + 5 \).
A) \( [-4, \infty) \)
B) \( [-3, \infty) \)
C) \( [5, \infty) \)
D) \( (-\infty, \infty) \)
8
What is the range of the function \( f(x) = -\sqrt{x-1} + 3 \)?
A) \( [3, \infty) \)
B) \( [1, \infty) \)
C) \( (-\infty, 3] \)
D) \( (-\infty, 1] \)
9
Determine the range of \( g(x) = 4 - 2^x \).
A) \( (4, \infty) \)
B) \( (-\infty, 4) \)
C) \( [4, \infty) \)
D) \( (-\infty, 4] \)
10
Which of the following is the domain of \( y = -x^2 + 10x \)?
A) \( [0, 10] \)
B) \( (-\infty, 25] \)
C) \( (-\infty, \infty) \)
D) \( [25, \infty) \)
11
Identify the domain of \( h(x) = \sqrt{3x + 9} \).
A) \( [3, \infty) \)
B) \( [-3, \infty) \)
C) \( (-\infty, -3] \)
D) \( [0, \infty) \)
12
What is the range of the function \( f(x) = (\frac{1}{3})^x - 5 \)?
A) \( (-5, \infty) \)
B) \( [-5, \infty) \)
C) \( (-\infty, -5) \)
D) \( (-\infty, \infty) \)
Version B Worksheet Function Frontiers
Domain & Range Practice • Version B
Name:
Date:
Instructions: For each function provided, identify the correct domain or range from the given options. Consider the characteristics of quadratic, square root, and exponential functions. Show any scratch work in the spaces provided.
1
What is the range of the function \( f(x) = 5^x - 3 \)?
A) \( (-\infty, \infty) \)
B) \( [-3, \infty) \)
C) \( (-3, \infty) \)
D) \( (0, \infty) \)
2
What is the domain of the function \( g(x) = \sqrt{x-6} + 2 \)?
A) \( [6, \infty) \)
B) \( [2, \infty) \)
C) \( (-\infty, 6] \)
D) \( (-\infty, \infty) \)
3
What is the domain of the function \( h(x) = -(x+1)^2 - 4 \)?
A) \( (-\infty, -4] \)
B) \( (-\infty, \infty) \)
C) \( [-1, \infty) \)
D) \( y \leq -4 \)
4
What is the range of the function \( f(x) = (x-2)^2 + 7 \)?
A) \( [7, \infty) \)
B) \( [2, \infty) \)
C) \( (-\infty, 7] \)
D) \( (-\infty, \infty) \)
5
What is the domain of the function \( j(x) = \sqrt{3x - 12} \)?
A) \( [0, \infty) \)
B) \( [4, \infty) \)
C) \( [-4, \infty) \)
D) \( (-\infty, 4] \)
6
Identify the domain of \( k(x) = 2 \cdot 3^{x-5} \).
A) \( [5, \infty) \)
B) \( (0, \infty) \)
C) \( (-\infty, \infty) \)
D) \( x \neq 5 \)
7
What is the range of the function \( f(x) = 4 - \sqrt{x} \)?
A) \( [4, \infty) \)
B) \( (-\infty, 4] \)
C) \( [0, 4] \)
D) \( (-\infty, \infty) \)
8
Find the range of \( f(x) = 2x^2 + 8x + 3 \).
A) \( [-5, \infty) \)
B) \( [-2, \infty) \)
C) \( [3, \infty) \)
D) \( (-\infty, \infty) \)
9
Determine the range of \( g(x) = (\frac{1}{2})^x + 6 \).
A) \( (6, \infty) \)
B) \( [6, \infty) \)
C) \( (0, \infty) \)
D) \( (-\infty, 6) \)
10
What is the domain of \( y = \sqrt{10 - x} \)?
A) \( [10, \infty) \)
B) \( [0, 10] \)
C) \( (-\infty, 10] \)
Function Frontiers Answer Key Answer Key
Function Frontiers • Version A
Problem 1: A
Problem 2: B
Problem 3: C
Problem 4: B
Problem 5: B
Problem 6: B
Problem 7: A
Problem 8: C
Problem 9: B
Problem 10: C
Problem 11: B
Problem 12: A
Answer Key
Function Frontiers • Version B
Problem 1: C
Problem 2: A
Problem 3: B
Problem 4: A
Problem 5: B
Problem 6: C
Problem 7: B
Problem 8: A
Problem 9: A
Problem 10: C
Problem 11: B
Problem 12: A
Version A Worksheet with Graphs Function Frontiers
Domain & Range Practice • Version A
Name:
Date:
Instructions: Analyze the function equation and its corresponding graph. Identify the correct domain or range from the options provided. Show your work or notes in the space provided.
1
What is the domain of the function \( f(x) = x^2 - 4x + 7 \)?
A) \( (-\infty, \infty) \)
B) \( [3, \infty) \)
C) \( [0, \infty) \)
D) \( (-\infty, 3] \)
Scratch work...
x y
2
What is the range of the function \( g(x) = \sqrt{x+5} - 2 \)?
A) \( [-5, \infty) \)
B) \( [-2, \infty) \)
C) \( (2, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
3
What is the range of the function \( h(x) = 3^x + 1 \)?
A) \( [1, \infty) \)
B) \( (-\infty, \infty) \)
C) \( (1, \infty) \)
D) \( (0, \infty) \)
Scratch work...
4
What is the range of the function \( f(x) = -2(x-3)^2 + 5 \)?
A) \( [5, \infty) \)
B) \( (-\infty, 5] \)
C) \( (-\infty, \infty) \)
D) \( [-2, 5] \)
Scratch work...
5
What is the domain of the function \( j(x) = \sqrt{8-2x} \)?
A) \( [4, \infty) \)
B) \( (-\infty, 4] \)
C) \( [0, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
6
What is the domain of the function \( k(x) = 0.5^{x+2} - 10 \)?
A) \( (-10, \infty) \)
B) \( (-\infty, \infty) \)
C) \( [-2, \infty) \)
D) \( x \neq -2 \)
Scratch work...
7
Find the range of \( f(x) = x^2 + 6x + 5 \).
A) \( [-4, \infty) \)
B) \( [-3, \infty) \)
C) \( [5, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
8
What is the range of the function \( f(x) = -\sqrt{x-1} + 3 \)?
A) \( [3, \infty) \)
B) \( [1, \infty) \)
C) \( (-\infty, 3] \)
D) \( (-\infty, 1] \)
Scratch work...
9
Determine the range of \( g(x) = 4 - 2^x \).
A) \( (4, \infty) \)
B) \( (-\infty, 4) \)
Version B Worksheet with Graphs Function Frontiers
Domain & Range Practice • Version B
Name:
Date:
Instructions: Analyze the function equation and its corresponding graph. Identify the correct domain or range from the options provided. Show your work or notes in the space provided.
1
What is the range of the function \( f(x) = 5^x - 3 \)?
A) \( (-\infty, \infty) \)
B) \( [-3, \infty) \)
C) \( (-3, \infty) \)
D) \( (0, \infty) \)
Scratch work...
2
What is the domain of the function \( g(x) = \sqrt{x-6} + 2 \)?
A) \( [6, \infty) \)
B) \( [2, \infty) \)
C) \( (-\infty, 6] \)
D) \( (-\infty, \infty) \)
Scratch work...
3
What is the domain of the function \( h(x) = -(x+1)^2 - 4 \)?
A) \( (-\infty, -4] \)
B) \( (-\infty, \infty) \)
C) \( [-1, \infty) \)
D) \( y \leq -4 \)
Scratch work...
4
What is the range of the function \( f(x) = (x-2)^2 + 7 \)?
A) \( [7, \infty) \)
B) \( [2, \infty) \)
C) \( (-\infty, 7] \)
D) \( (-\infty, \infty) \)
Scratch work...
5
What is the domain of the function \( j(x) = \sqrt{3x - 12} \)?
A) \( [0, \infty) \)
B) \( [4, \infty) \)
C) \( [-4, \infty) \)
D) \( (-\infty, 4] \)
Scratch work...
6
Identify the domain of \( k(x) = 2 \cdot 3^{x-5} \).
A) \( [5, \infty) \)
B) \( (0, \infty) \)
C) \( (-\infty, \infty) \)
D) \( x \neq 5 \)
Scratch work...
7
What is the range of the function \( f(x) = 4 - \sqrt{x} \)?
A) \( [4, \infty) \)
B) \( (-\infty, 4] \)
C) \( [0, 4] \)
D) \( (-\infty, \infty) \)
Scratch work...
8
Find the range of \( f(x) = 2x^2 + 8x + 3 \).
A) \( [-5, \infty) \)
B) \( [-2, \infty) \)
C) \( [3, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
9
Determine the range of \( g(x) = (\frac{1}{2})^x + 6 \).
A) \( (6, \infty) \)
B) \( [6, \infty) \)
C) \( (0, \infty) \)
Version A Worksheet with Graph Numbers Function Frontiers
Domain & Range Practice • Version A
Name:
Date:
Instructions: Analyze the function equation and its corresponding graph. Identify the correct domain or range from the options provided. Show your work or notes in the space provided.
1
What is the domain of the function \( f(x) = x^2 - 4x + 7 \)?
A) \( (-\infty, \infty) \)
B) \( [3, \infty) \)
C) \( [0, \infty) \)
D) \( (-\infty, 3] \)
Scratch work...
-10 -5 5 10 10 5 -5 -10 x y
2
What is the range of the function \( g(x) = \sqrt{x+5} - 2 \)?
A) \( [-5, \infty) \)
B) \( [-2, \infty) \)
C) \( (2, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
-5 5 5 -5
3
What is the range of the function \( h(x) = 3^x + 1 \)?
A) \( [1, \infty) \)
B) \( (-\infty, \infty) \)
C) \( (1, \infty) \)
D) \( (0, \infty) \)
Scratch work...
-5 5 5 -5
4
What is the range of the function \( f(x) = -2(x-3)^2 + 5 \)?
A) \( [5, \infty) \)
B) \( (-\infty, 5] \)
C) \( (-\infty, \infty) \)
D) \( [-2, 5] \)
Scratch work...
-5 5 5 -5
5
What is the domain of the function \( j(x) = \sqrt{8-2x} \)?
A) \( [4, \infty) \)
B) \( (-\infty, 4] \)
C) \( [0, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
-5 5 5 -5
6
What is the domain of the function \( k(x) = 0.5^{x+2} - 10 \)?
A) \( (-10, \infty) \)
B) \( (-\infty, \infty) \)
C) \( [-2, \infty) \)
D) \( x \neq -2 \)
Scratch work...
-5 5 10 5
7
Find the range of \( f(x) = x^2 + 6x + 5 \).
A) \( [-4, \infty) \)
B) \( [-3, \infty) \)
C) \( [5, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
-5 5 5 -5
8
What is the range of the function \( f(x) = -\sqrt{x-1} + 3 \)?
A) \( [3, \infty) \)
B) \( [1, \infty) \)
C) \( (-\infty, 3] \)
D) \( (-\infty, 1] \)
Version B Worksheet with Graph Numbers Function Frontiers
Domain & Range Practice • Version B
Name:
Date:
Instructions: Analyze the function equation and its corresponding graph. Identify the correct domain or range from the options provided. Show your work or notes in the space provided.
1
What is the range of the function \( f(x) = 5^x - 3 \)?
A) \( (-\infty, \infty) \)
B) \( [-3, \infty) \)
C) \( (-3, \infty) \)
D) \( (0, \infty) \)
Scratch work...
-5 5 5 -5
2
What is the domain of the function \( g(x) = \sqrt{x-6} + 2 \)?
A) \( [6, \infty) \)
B) \( [2, \infty) \)
C) \( (-\infty, 6] \)
D) \( (-\infty, \infty) \)
Scratch work...
5 10 5 -5
3
What is the domain of the function \( h(x) = -(x+1)^2 - 4 \)?
A) \( (-\infty, -4] \)
B) \( (-\infty, \infty) \)
C) \( [-1, \infty) \)
D) \( y \leq -4 \)
Scratch work...
-5 5 -5
4
What is the range of the function \( f(x) = (x-2)^2 + 7 \)?
A) \( [7, \infty) \)
B) \( [2, \infty) \)
C) \( (-\infty, 7] \)
D) \( (-\infty, \infty) \)
Scratch work...
5 10 10 5
5
What is the domain of the function \( j(x) = \sqrt{3x - 12} \)?
A) \( [0, \infty) \)
B) \( [4, \infty) \)
C) \( [-4, \infty) \)
D) \( (-\infty, 4] \)
Scratch work...
4 10 5
6
Identify the domain of \( k(x) = 2 \cdot 3^{x-5} \).
A) \( [5, \infty) \)
B) \( (0, \infty) \)
C) \( (-\infty, \infty) \)
D) \( x \neq 5 \)
Scratch work...
5 10 5
7
What is the range of the function \( f(x) = 4 - \sqrt{x} \)?
A) \( [4, \infty) \)
B) \( (-\infty, 4] \)
C) \( [0, 4] \)
D) \( (-\infty, \infty) \)
Scratch work...
5 10 4
8
Find the range of \( f(x) = 2x^2 + 8x + 3 \).
A) \( [-5, \infty) \)
B) \( [-2, \infty) \)
C) \( [3, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
Version A Worksheet with Graph Numbers Revised Function Frontiers
Domain & Range Practice • Version A
Name:
Date:
Instructions: Analyze the function equation and its corresponding graph. Identify the correct domain or range from the options provided. Show your work or notes in the space provided.
1
What is the domain of the function \( f(x) = x^2 - 4x + 7 \)?
A) \( (-\infty, \infty) \)
B) \( [3, \infty) \)
C) \( [0, \infty) \)
D) \( (-\infty, 3] \)
Scratch work...
-5 5 5 -5
2
What is the range of the function \( g(x) = \sqrt{x+5} - 2 \)?
A) \( [-5, \infty) \)
B) \( [-2, \infty) \)
C) \( (2, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
-5 5 5 -5
3
What is the range of the function \( h(x) = 3^x + 1 \)?
A) \( [1, \infty) \)
B) \( (-\infty, \infty) \)
C) \( (1, \infty) \)
D) \( (0, \infty) \)
Scratch work...
-5 5 5
4
What is the range of the function \( f(x) = -2(x-3)^2 + 5 \)?
A) \( [5, \infty) \)
B) \( (-\infty, 5] \)
C) \( (-\infty, \infty) \)
D) \( [-2, 5] \)
Scratch work...
5 5
5
What is the domain of the function \( j(x) = \sqrt{8-2x} \)?
A) \( [4, \infty) \)
B) \( (-\infty, 4] \)
C) \( [0, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
-5 5 4 5
6
What is the domain of the function \( k(x) = 0.5^{x+2} - 10 \)?
A) \( (-10, \infty) \)
B) \( (-\infty, \infty) \)
C) \( [-2, \infty) \)
D) \( x \neq -2 \)
Scratch work...
-5 5 10
7
Find the range of \( f(x) = x^2 + 6x + 5 \).
A) \( [-4, \infty) \)
B) \( [-3, \infty) \)
C) \( [5, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
-3 5 -4
8
What is the range of the function \( f(x) = -\sqrt{x-1} + 3 \)?
A) \( [3, \infty) \)
B) \( [1, \infty) \)
C) \( (-\infty, 3] \)
D) \( (-\infty, 1] \)
Version B Worksheet with Graph Numbers Revised Function Frontiers
Domain & Range Practice • Version B
Name:
Date:
Instructions: Analyze the function equation and its corresponding graph. Identify the correct domain or range from the options provided. Show your work or notes in the space provided.
1
What is the range of the function \( f(x) = 5^x - 3 \)?
A) \( (-\infty, \infty) \)
B) \( [-3, \infty) \)
C) \( (-3, \infty) \)
D) \( (0, \infty) \)
Scratch work...
-3
2
What is the domain of the function \( g(x) = \sqrt{x-6} + 2 \)?
A) \( [6, \infty) \)
B) \( [2, \infty) \)
C) \( (-\infty, 6] \)
D) \( (-\infty, \infty) \)
Scratch work...
6 2
3
What is the domain of the function \( h(x) = -(x+1)^2 - 4 \)?
A) \( (-\infty, -4] \)
B) \( (-\infty, \infty) \)
C) \( [-1, \infty) \)
D) \( y \leq -4 \)
Scratch work...
-1 -4
4
What is the range of the function \( f(x) = (x-2)^2 + 7 \)?
A) \( [7, \infty) \)
B) \( [2, \infty) \)
C) \( (-\infty, 7] \)
D) \( (-\infty, \infty) \)
Scratch work...
2 7
5
What is the domain of the function \( j(x) = \sqrt{3x - 12} \)?
A) \( [0, \infty) \)
B) \( [4, \infty) \)
C) \( [-4, \infty) \)
D) \( (-\infty, 4] \)
Scratch work...
4
6
Identify the domain of \( k(x) = 2 \cdot 3^{x-5} \).
A) \( [5, \infty) \)
B) \( (0, \infty) \)
C) \( (-\infty, \infty) \)
D) \( x \neq 5 \)
Scratch work...
5
7
What is the range of the function \( f(x) = 4 - \sqrt{x} \)?
A) \( [4, \infty) \)
B) \( (-\infty, 4] \)
C) \( [0, 4] \)
D) \( (-\infty, \infty) \)
Scratch work...
5 4
8
Find the range of \( f(x) = 2x^2 + 8x + 3 \).
A) \( [-5, \infty) \)
B) \( [-2, \infty) \)
C) \( [3, \infty) \)
D) \( (-\infty, \infty) \)
Scratch work...
-2 -5
