Math Core

This test covers parent functions and transformations, piecewise and absolute value functions, and systems of linear equations in three variables.

Question 1

How does the graph of $g(x) = (x + 2)^2 - 3$ relate to the graph of $f(x) = x^2$ ?

Question 2

What is the vertex of $g(x) = -\lvert x - 5 \rvert + 1$ ?

Enter a point like (2, -3)

Question 3

For $x \ge 0$ , which function has the same graph as $g(x) = \sqrt{4x}$ ?

Question 4

What is the range of $g(x) = -2\sqrt{x + 1} + 6$ ? Write it as an inequality in $y$ .

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

Question 5

The point $(-2, 5)$ is on the graph of $f$ . What point must be on the graph of $g(x) = 2f(x + 4) - 1$ ?

Enter a point like (2, -3)

Question 6

The graph of $f(x) = x^3$ is reflected across the $x$ -axis, then shifted right $1$ unit and up $2$ units. Write the new function $g(x)$ .

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

Question 7

Let $f(x) = \begin{cases} x^2 - 1, & x < 0 \\ 2x + 3, & x \ge 0 \end{cases}$ . Find $f(-3) + f(0)$ .

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

Question 8

Find both $x$ -intercepts of $f(x) = 2\lvert x - 1 \rvert - 6$ .

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

Question 9

Which piecewise function is equal to $g(x) = 3\lvert x + 1 \rvert - 2$ ?

Question 10

Which function is graphed below?

A piecewise graph with three pieces.Open in grapher →

Question 11

The graph of $f(x) = a\lvert x + 2 \rvert - 1$ passes through $(1, 11)$ . Find $a$ .

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

Question 12

Solve the system. Enter your answer as $(x, y, z)$ .

\begin{aligned} x + y + z &= 4 \\ 2x - y + z &= 9 \\ x + 2y - 3z &= -5 \end{aligned}

Enter a point like (2, -3)

Question 13

How many solutions does this system have?

\begin{aligned} x + y + z &= 2 \\ x + 2y - z &= 5 \\ 2x + 3y &= 10 \end{aligned}

Question 14

The parabola $y = ax^2 + bx + c$ passes through $(-1, 4)$ , $(1, 0)$ and $(2, 1)$ . Find $a$ , $b$ and $c$ . Enter your answer as $(a, b, c)$ .

Enter a point like (2, -3)

Question 15

A jar holds $30$ coins, all nickels, dimes and quarters, worth $4.40 in total. There are $4$ more quarters than nickels. How many dimes are in the jar?

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