Function Foundations Quiz
Algebra I Assessment
Function Foundations Quiz
Name:
Date:
Period:
Score: / 36
Directions: Read each question carefully. Show all necessary work and label your answers clearly.
Part 1: Relations & Functions 6 Points (3 pts each)
1. Function or Not? [3 pts]
Determine if the mapping diagram represents a function. Explain your reasoning.
Input (x) -2 1 4 Output (y) 3 7
Is it a function?
Yes No
Reason:
2. Vertical Line Test [3 pts]
Which graph does NOT represent a function? Circle the letter and justify below.
A
B
C
D
Reason: Passes / fails vertical line test because:
Part 2: Independent & Dependent Variables 6 Points (3 pts each)
3. Contextual Variables [3 pts]
A private math tutor charges a flat registration fee of $25 plus $30 for each hour of tutoring. The total cost \(C\) depends on the number of hours \(h\) tutored.
Independent Variable:
Dependent Variable:
Equation \(C(h)\):
4. Interpreting Notation [3 pts]
The function \(G(d) = 50 - 0.04d\) models the gallons of fuel \(G\) remaining in a truck after driving \(d\) miles.
a. Identify which variable is independent:
b. Explain what the statement \(G(250) = 40\) means in words:
Part 3: Domain & Range 6 Points (3 pts each)
5. Discrete Relation [3 pts]
Given the set of ordered pairs representing relation \(R\):
\(R = \{(-4, 3), \; (-1, 5), \; (0, -2), \; (2, 3), \; (5, -6)\}\)
Domain: { list values in order }
Range: { do not repeat values }
6. Continuous Graph [3 pts]
Find the domain and range of the graphed segment using inequalities or interval notation.
x y
Domain: left to right \(x\)-values
Range: bottom to top \(y\)-values
Function Foundations Quiz • Algebra I Page 1 of 2
Algebra I Assessment
Function Foundations Quiz — Page 2
Student Name:
Period:
Part 4: Linear vs. Non-Linear Relationships 6 Points (3 pts each)
7. Analyzing Tables [3 pts]
Determine whether the table represents a Linear or Non-linear function by checking the rate of change.
Linear Non-linear
Rate of Change (\(\frac{\Delta y}{\Delta x}\)):
Justification:
8. Equation Classification [3 pts]
Classify each equation as Linear (L) or Non-linear (NL) and explain how you know.
a. \(f(x) = 4 - 3x\)
Type:
b. \(g(x) = 2x^2 + 5\)
Type:
Explanation of difference:
Part 5: Function Notation & Graphing 18 Points (Q9-Q10: 4 pts each, Q11: 6 pts, Q12: 4 pts)
9. Evaluating Functions [4 pts]
Given the functions \(f(x) = -3x + 7\) and \(g(x) = \frac{1}{2}x - 4\):
a. Find \(f(5)\):
b. Find \(x\) when \(g(x) = 2\):
10. Complete Function Table [4 pts]
Complete the input-output table for \(h(x) = 2x - 3\):
11. Graphing in Function Notation [6 pts]
Graph the linear function: \(f(x) = -\frac{3}{2}x + 3\)
Plot at least 3 integer points and draw the continuous line with arrows.
x y
\(y\)-intercept: (0, ____)
Slope (\(m\)): ________
12. Reading Function Graphs [4 pts]
Use the given graph of \(k(x)\) to answer each question.
k(x) x y
a. Find \(k(0)\):
b. Find \(k(4)\):
c. Find \(x\) when \(k(x) = 0\):
Function Foundations Quiz • Algebra I Page 2 of 2
