Function Foundations Review Worksheet
Function Foundations
Unit 1 Test Prep & Review
Name:
Date:
Part 1: Vocabulary Toolkit
Match the term on the left with its correct definition on the right by drawing a line.
1. Slope (m)
2. y-intercept (b)
3. Domain
4. Range
5. Function
6. Linear Function
7. Variable
The set of all possible input values (\(x\)-values).
The starting point on a graph where \(x=0\).
A letter used to represent an unknown number.
The steepness of a line (Rise over Run).
A relationship where every input has exactly one output.
A function that forms a straight line when graphed.
The set of all possible output values (\(y\)-values).
Part 2: Plotting & Graphing
8. Write the equation for this line:
Slope (\(m\)): ____________________
\(y\)-intercept (\(b\)): ________________
y =
9. Write the equation for this line:
Slope (\(m\)): ____________________
\(y\)-intercept (\(b\)): ________________
y =
Part 2: Plotting & Graphing (Continued)
10. Graph: \(f(x) = \frac{2}{3}x + 1\)
Use a ruler to draw a straight line.
11. Graph: \(f(x) = -2x - 4\)
Use a ruler to draw a straight line.
Part 3: Decoding Word Problems
12. Fitness Club: A club charges a $40 sign-up fee and $25 per month. Let \(M\) be the number of months and \(C\) be the total cost.
Function Notation:
C(M) =
Total cost for 10 months:
13. Taxi Ride: A taxi costs $5.00 just to get in, plus $2.50 per mile traveled. Let \(d\) be distance and \(T\) be total fare.
Function Notation:
T(d) =
Fare for a 12-mile ride:
14. Savings: Sarah starts with $150 and saves $20 every week. Let \(w\) be the weeks and \(S\) be the total savings.
Function Notation:
S(w) =
Weeks to reach $450?
Part 4: Functions & Domain
15. If \(f(x) = 5x - 8\), find \(f(3)\).
Answer: _________________
16. If \(g(x) = -2x + 12\), find \(g(5)\).
Answer: _________________
17. If \(h(x) = \frac{1}{2}x + 4\), find \(h(10)\).
Answer: _________________
18. If \(f(x) = 3x + 1\), find \(x\) when \(f(x) = 16\).
Answer: _________________
Part 4: Functions & Domain (Continued)
19. Use the graph to find \(f(2)\) and \(f(-2)\):
\(f(2)\) = _______
\(f(-2)\) = _______
20. Identify Domain & Range:
{(−1, 4), (0, 2), (2, 2), (5, −3)}
Domain: ______________________
Range: _______________________
Part 5: Point to Equation Challenge
21. Write the equation through: (0, 4) and (2, 10)
Step 1: Slope (m)
Step 2: Intercept (b)
Step 3: Equation
y =
22. Write the equation through: (3, 5) and (6, 4)
Step 1: Slope (m)
Step 2: Intercept (b)
Step 3: Equation
y =
23. Write the equation through: (-1, 2) and (1, 6)
Step 1: Slope (m)
Step 2: Intercept (b)
Step 3: Equation
y =
Function Foundations Answer Key
Answer Key
Function Foundations Review
Teacher Resource
Part 1: Vocabulary Toolkit
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1. Slope: Steepness of a line (Rise/Run)
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2. y-intercept: Starting point where \(x=0\)
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3. Domain: Set of all input values (\(x\))
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4. Range: Set of all output values (\(y\))
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5. Function: Relationship with exactly one output per input
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6. Linear Function: Function that forms a straight line
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7. Variable: Letter representing an unknown number
Part 2: Plotting & Graphing
8. Equation: \(m = 1/2\), \(b = 2\) \(\rightarrow\) y = 1/2x + 2
9. Equation: \(m = 2\), \(b = -3\) \(\rightarrow\) y = 2x - 3
10. Graph \(f(x) = 2/3x + 1\): Plot (0,1), go UP 2, RIGHT 3.
11. Graph \(f(x) = -2x - 4\): Plot (0,-4), go DOWN 2, RIGHT 1.
Part 3: Decoding Word Problems
12. Fitness: \(C(M) = 25M + 40\). Cost for 10: \(25(10) + 40 = \mathbf{\$290}\).
13. Taxi: \(T(d) = 2.50d + 5.00\). Fare for 12: \(2.50(12) + 5 = \mathbf{\$35}\).
14. Savings: \(S(w) = 20w + 150\). Reach $450: \(450 = 20w + 150 \rightarrow 300 = 20w \rightarrow \mathbf{w = 15}\).
Part 4: Functions & Domain
15. f(3): \(5(3) - 8 = \mathbf{7}\)
16. g(5): \(-2(5) + 12 = \mathbf{2}\)
17. h(10): \(1/2(10) + 4 = \mathbf{9}\)
18. Solve x: \(3x + 1 = 16 \rightarrow \mathbf{x = 5}\)
19. Graph: \(f(2) = \mathbf{-2}\) | \(f(-2) = \mathbf{2}\)
20. Set: Domain: \(\{-1, 0, 2, 5\}\) | Range: \(\{-3, 2, 4\}\)
Part 5: Point to Equation Challenge
21. (0, 4) and (2, 10): \(b=4\), \(m = 6/2 = 3\). \(\rightarrow\) y = 3x + 4
22. (3, 5) and (6, 4): \(m = -1/3\). \(5 = -1/3(3) + b \rightarrow b = 6\). \(\rightarrow\) y = -1/3x + 6
\(m = 4/2 = 2\). \(6 = 2(1) + b \rightarrow b = 4\). \(\rightarrow\)
