Math Core

This test covers all of Unit 4: relations and functions, function notation, domain and range, reading graphs of functions, and arithmetic sequences.

Question 1

Which relation is not a function?

Question 2

Which equation's graph passes the vertical line test?

Question 3

Let $f(x) = 2x^2 - 3x$ . Find $f(-2)$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

Let $g(x) = 7 - 3x$ . For what value of $x$ is $g(x) = -8$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 5

Let $f(x) = 3x + 1$ . Find $f(a - 2)$ in terms of $a$ .

Enter an expression, e.g. 3x^2 - 2x + 1

Question 6

The temperature of a cup of cocoa, in degrees Fahrenheit, $m$ minutes after it is poured is modeled by $T(m) = 180 - 4m$ for the first $20$ minutes. What does $T(5) = 160$ mean?

Question 7

List the domain of the relation $\{(3, -1), (-2, 4), (0, 4), (6, 9)\}$ .

Separate answers with commas, e.g. 2, -5

Question 8

Find the range of $f(x) = -(x - 1)^2 + 4$ , graphed below. Write your answer as an inequality in $y$ .

The parabola y = −(x − 1)² + 4.Open in grapher →

Enter an inequality, e.g. x >= 4, -2 < x <= 3, or x < 1 or x > 5

Question 9

Find the domain of $h(x) = \sqrt{x - 4}$ . Write your answer as an inequality in $x$ .

Enter an inequality, e.g. x >= 4, -2 < x <= 3, or x < 1 or x > 5

Question 10

The graph below shows a function from $(-3, 2)$ to $(2, -3)$ , with both endpoints included. What are its domain and range?

A line segment from (−3, 2) to (2, −3).Open in grapher →

Question 11

A food truck can make at most $150$ tacos a day and sells them for $3 each. Daily taco revenue is $R(t) = 3t$ dollars for $t$ tacos sold. Which is the reasonable domain?

Problems 12 to 14 use the graph of $f(x) = x^2 - 4x$ below.

The graph of y = f(x).Open in grapher →

Question 12

List the zeros of $f$ .

Separate answers with commas, e.g. 2, -5

Question 13

Where is $f$ decreasing?

Question 14

Use the graph to solve $f(x) = 5$ .

Separate answers with commas, e.g. 2, -5

Question 15

Find the $30$ th term of the arithmetic sequence $12, 9, 6, 3, \ldots$

Enter a number. Fractions like 3/4 and sqrt(2) are OK.