Question 1

Solve the following system of equations: 
$$\begin{cases} 2x + 5y = 2 \ 3x - 4y = 20 \end{cases}$$

Accepted Answer

$$x = 4, y = -2$$

Question 2

Find the distance between the points $$(-2, 3)$$ and $$(3, -9).$$

Accepted Answer

$$\sqrt{170}$$

Question 3

What is the midpoint between the points $$(2, 6)$$ and $$(-1, 4)$$?

Accepted Answer

$$(0.5, 5)$$

Question 4

Given $$f(x) = 5x^2$ - 7x$$, find $$f(3).$$

Accepted Answer

$$5(9) - 7(3) = 45 - 21 = 24$$

Question 5

Given $$g(x) = 3x^2$ - 5x + 2$$, find $$g(-1).$$

Accepted Answer

$$3(-1)^2 - 5(-1) + 2 = 3 + 5 + 2 = 10$

Question 6

Given $$g(x) = \begin{cases} \sqrt{x+4} & x \geq 4 \ x+4 & x \u003c 4 \end{cases}$$, find $$g(3).$$

Accepted Answer

$$7$$

Question 7

Determine if the function $$f(x) = x^3$ - 5x is $$even, odd, or neither.

Accepted Answer

Odd

Question 8

Find and simplify the difference quotient for $$f(x) = 2x^2$ + x + 10.$$

Accepted Answer

$$4x + 2h + 1$$

Question 9

Find the domain of $$f(x) = \dfrac{2x}{x^2$ - 9}.$$

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Question 10

Given $$f(x) = x^2$ + 1$$, $$g(x) = 2x + 1$$, find $$(f \circ g)(2).$$

Accepted Answer

$$(2 \cdot 2 + 1)^2$ + 1 = 5^2$ + 1 = 26$$

Question 11

Given $$f(x) = x^2$ + 3$$, $$g(x) = x - 1$$, find $$f(g(x)).$$

Accepted Answer

$$(x-1)^2 + 3$

Question 12

Determine if $$f(x) = 2x - 5$$ and $$g(x) = \dfrac{x+5}{2}$$ are inverses.

Accepted Answer

Yes, because $$f(g(x)) = x$$ and $$g(f(x)) = x$$

Question 13

Find the inverse of $$f(x) = 4x + 8.$$

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x-8}{4}$$

Question 14

Given the center $$(-2, 4)$$ and radius $$r = 5$$, write the standard form of the equation of a circle.

Accepted Answer

$$(x+2)^2$$ + $$(y-4)^2 = 25$

Question 15

Find the average rate of change of $$f(x) = x^2$ + x$$ from $$x = 2 to$$ $$x = 5.$$

Accepted Answer

$$\dfrac{f(5) - f(2)}{5-2} = \dfrac{30 - 6}{3} = 8$$

Question 16

Which of the following best describes the domain of $$f(x) = \sqrt{x-4}$$?

Accepted Answer

$$[4, \infty)$$

Question 17

If $$f(x) = |x|$$ and $$g(x) = |x-1| - 4$$, which statement is true about their graphs?

Accepted Answer

$$g(x) is $$the graph of $$f(x)$$ shifted right by 1 and down by 4

Question 18

Graph the quadratic function $$f(x) = -2(x-3)^2$ + 8. $$What is the vertex?

Accepted Answer

$$(3, 8)$$

Question 19

Given the graph of a function, which of the following is NOT a possible $$x-$$intercept?

Accepted Answer

$$(0, 2)$$

Precalculus Midterm Review: Step-by-Step Study Guidance

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