Question 1

Given $$f(x) = 2x + 3$$ and $$g(x) = x^2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 3$

Question 2

If $$h(x) = x - 4$$ and $$k(x) = 5x$$, find $$(k \circ h)(2).$$

Accepted Answer

$$10$$

Question 3

Which of the following is the correct order of operations for the composition $$(f \circ g)(x)$$?

Accepted Answer

First apply $$g$$, then $$f$$

Question 4

Suppose $$f(x) = x^2$ and g(x) = x + 1$. What is (g$$ \circ f)(x)$$?

Accepted Answer

$$x^2 + 1$

Question 5

A function $$f(x)$$ passes through the point $$(2, 5). If $$you apply the transformation $$g(x) = f(x - 3)$$, what is the new $$x-$$coordinate of the corresponding point?

Accepted Answer

$$-1$$

Question 6

Which transformation reflects a function $$f(x)$$ over the $$y-$$axis?

Accepted Answer

$$f(-x)$$

Question 7

Given $$f(x) = x^2$ - 4x + 3$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -1)$$

Question 8

Which of the following is NOT a possible form of a quadratic function?

Accepted Answer

$$f(x) = ax^3$ + bx^2$ + c$$

Question 9

If a quadratic function $$f(x) is $$given in factored form $$f(x) = a(x - r_1$)(x - r_2$)$$, what do $$r_1$$ and $$r_2$$ represent?

Accepted Answer

The $$x-$$intercepts

Question 10

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 1. $$What is the maximum height reached by the ball?

Accepted Answer

$$41$$ meters

Question 11

Which transformation shifts the graph of $$f(x) up by$$ $$c$$ units?

Accepted Answer

$$f(x) + c$$

Question 12

Given $$f(x) = (x - 2)^2$ + 5$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 13

If $$f(x) is an $$even function and $$g(x) is an $$odd function, which of the following is always true?

Accepted Answer

$$f(-x) = f(x)$$ and $$g(-x) = -g(x)$$

Question 14

A quadratic function $$f(x)$$ has its vertex at $$(3, -2)$$ and opens upward. Which is a possible equation for $$f(x)$$?

Accepted Answer

$$f(x) = a(x - 3)^2$ - 2$$ with $$a \u003e 0$$

Question 15

If $$f(x) = x^2$ - 6x + 8$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 16

Which of the following transformations will compress the graph of $$f(x)$$ vertically by a factor of $$\frac{1}{2}$$?

Accepted Answer

$$\frac{1}{2}f(x)$$

Question 17

Given $$f(x) = x^2$ + 4x + 7$$, convert $$f(x) to $$vertex form.

Accepted Answer

$$f(x) = (x + 2)^2$ + 3$$

Question 18

A quadratic function $$f(x)$$ does not have a factored form. Which of the following is a possible reason?

Accepted Answer

The discriminant $$b^2 - 4ac$$ \u003c 0$$

Question 19

If $$f(x) = x^2$ - 2x + 1$$, what is the minimum value of $$f(x)$$ and at what $$x$$ does it occur?

Accepted Answer

Minimum is $$0 at$$ $$x = 1$$

Precalculus Study Guide: Function Composition, Transformations, and Quadratic Functions

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