$$[\text{minimum value}, \infty)$$

Question 1

Which of the following equations is NOT a function when graphed in the Cartesian plane?

Accepted Answer

$$x^2$$ + $$y^2 = 4$

Question 2

Given the quadratic equation $$3x^2 + 6x - 9 = 0$, what are the solutions for x$?

Accepted Answer

$$x = \dfrac{-6 \pm \sqrt{144}}{6}$$

Question 3

Which of the following describes the domain of the function $$f(x) = \sqrt{x-5}$$?

Accepted Answer

$$x \geq 5$$

Question 4

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f + g)(x$$)$$?

Accepted Answer

$$x^2 + x + 1$

Question 5

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 6

The graph of $$y = f(x) is $$reflected about the $$x-$$axis. Which equation represents the new graph?

Accepted Answer

$$y = -f(x)$$

Question 7

What is the range of the function $$f(x) = 2x^2$ - 5x + 2$$?

Accepted Answer

$$[	ext{minimum value}, \infty)$$

Question 8

Which of the following is the correct binomial expansion for $$(x + a)^2$?

Accepted Answer

$$x^2 + 2xa$$ + $$a^2$$

Question 9

Given $$f(x) = x^3$ and g(x) = x - 2$, what is the composite function (f$$ \circ g)(x)$$?

Accepted Answer

$$f(g(x)) = (x - 2)^3$

Question 10

Which of the following is true about the exponential function $$f(x) = a^x$$ where $$a \u003e 0$$?

Accepted Answer

The range is $$(0, \infty)$$

Question 11

If $$f(x) is an $$even function, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$

Question 12

Which of the following is the correct factorization for $$x^3$$ + $$a^3$$?

Accepted Answer

$$(x + a)(x^2$ - ax + a^2$)$$

Question 13

A function $$f(x) is $$defined as $$f(x) = |x|. $$Which of the following statements is true?

Accepted Answer

$$f(x) is $$even

Question 14

Which transformation will shift the graph of $$y = f(x)$$ three units to the right?

Accepted Answer

$$y = f(x - 3)$$

Question 15

Given the function $$f(x) = \frac{1}{x - 2}$$, what is the domain?

Accepted Answer

$$x 
eq 2$$

Question 16

Which of the following is the correct factorization for $$x^2 + 2x + 1$?

Accepted Answer

$$(x + 1)^2$

Question 17

If $$f(x) = x^2$ and g(x) = 2x$, what is (f$$ \cdot g)(x)$$?

Accepted Answer

$$2x^3$$

Question 18

Which of the following is the correct formula for the quadratic formula?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 19

Which of the following is the correct expansion for $$(x - a)^3$?

Accepted Answer

$$x^3$$ - $$3x^2a$$ + $$3xa^2$$ - $$a^3$$

Question 20

Which of the following statements about the Cartesian plane is correct?

Accepted Answer

The origin is the point $$(0, 0)$$ where the $$x-$$axis and $$y-$$axis intersect.

Algebraic Foundations: Special Products, Factorization, and Functions

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