Question 1

Which of the following relations defines a function from set $$X to $$set $$Y$$?

Accepted Answer

Each element in $$X is $$assigned to exactly one element in $$Y.$$

Question 2

Given $$f(x) = x^2$, evaluate $$\frac{f(x+h) - f(x)}{h}$$ and simplify.

Accepted Answer

$$2x + h$$

Question 3

Which equation fails the vertical line test and does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$y^3$$ = $$x^2$$

Question 4

Let $$f(x) = x^2$ and g(x) = x + 2$. What is (f$$ \cdot g)(x)$$?

Accepted Answer

$$x^2(x + 2$$)$$

Question 5

Which of the following functions is even?

Accepted Answer

$$f(x) = x^4$ + 2x^2$

Question 6

For the function $$f(x) = x^2$ - 3x + 2$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 1$$ and $$x = 2$$

Question 7

Which transformation results in a vertical shift up by $$k$$ units for a function $$f(x)$$?

Accepted Answer

$$f(x) + k$$

Question 8

Given the piecewise function $$f(x) = \begin{cases} 3x + 5 & x \u003c 0 \ 4x + 7 & x \geq 0 \end{cases}$$, what is $$f(3)$$?

Accepted Answer

$$19$$

Question 9

A cellphone company charges $$30$$ dollars for up to $$120$$ minutes, and $$0.30$$ per minute thereafter. What is the cost for $$150$$ minutes?

Accepted Answer

$$39$$

Question 10

Which function is symmetric with respect to the origin?

Accepted Answer

$$f(x) = x^3$

Question 11

For the quadratic function $$f(x) = ax^2$ + bx + c$$, what is the formula for the vertex?

Accepted Answer

$$\left( -\frac{b}{2a}, f\left( -\frac{b}{2a} \right) \right)$$

Question 12

If $$f(x) = x^2$ is transformed to g(x) = (x$$ - $$2)^2 - 2$, what is the new vertex?

Accepted Answer

$$(2, -2)$$

Question 13

A farmer has $$800$$ feet of fencing to enclose a rectangular field. Express the area $$A as a $$function of one side $$x.$$

Accepted Answer

$$A(x) = x \left( \frac{800 - 2x}{2} \right)$$

Question 14

Given $$S = -1000 + 100p$$ and $$D = 5000 - 200p$$, what is the equilibrium price $$p$$?

Accepted Answer

$$p = 20$$

Question 15

For the function $$f(x) = \sqrt{x^2$ - 6x}$$, what is the domain?

Accepted Answer

$$x \leq 0 or$$ $$x \geq 6$$

Question 16

A wire of length $$20 ft is $$cut into two pieces. One is bent into a circle, the other into a square. If $$x is $$the length of the piece for the circle, what is the total area as a function of $$x$$?

Accepted Answer

$$A(x) = \frac{x^2$}{4\pi} + \frac{(20 - x)^2$}{16}$$

Question 17

For the quadratic inequality $$4x^2 - 6x$$ \u003c -9$$, what is the solution set?

Accepted Answer

$$-0.75 \u003c x \u003c 3$$

Question 18

If $$f(x) = |x| + 2$$, which transformation has been applied to $$f(x) = |x|$$?

Accepted Answer

Vertical shift up by $$2$$ units

Question 19

Given the function $$f(x) = x - 1$$ and $$g(x) = -2x + 2$$, solve $$f(x) = g(x).$$

Accepted Answer

$$x = 1$$

Functions and Quadratic Functions: Definitions, Properties, Graphs, and Applications

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