Question 1

Which of the following sets represents a function?

$$\{(2, 5), (3, 7), (2, 8), (4, 1)\}$$

Accepted Answer

No, because the input $$2 is $$paired with two different outputs.

Question 2

Find the domain of the function $$f(x) = \sqrt{x - 5}.$$

Accepted Answer

$$x \geq 5$$

Question 3

Given $$f(x) = -3x + 5$$, for which value of $$x$$ does $$f(x) = -19$$?

Accepted Answer

$$x = 8$$

Question 4

Which of the following is the correct simplification of $$(4 - 6i)(2 + 3i)$$?

Accepted Answer

Question 5

Solve the quadratic equation $$x^2 - 20x + 30 = 3x$$ - $$2x^2.$$

Accepted Answer

$$x = -2, x = 15$$

Question 6

For the quadratic function $$f(x) = 2x^2$ + 5x - 12$$, which statement is true?

Accepted Answer

The parabola opens upward and the vertex is at $$\left(-\frac{5}{4}, -15.125\right).$$

Question 7

A rancher has a rectangular piece of sheet metal 20 inches wide and 10 feet long. He folds up the sides to form a trough. If $$x is $$the height of the sides, what value of $$x$$ maximizes the volume?

Accepted Answer

$$x = 5$$ inches

Question 8

Given $$f(x) = 3x - 5$$ for $$x \leq -5$$, $$f(x) = 6$$ for $$-5  3$$, what is $$f(5)$$?

Accepted Answer

$$-3$$

Question 9

Which of the following describes all transformations applied to $$g(x) = 2|x - 1| - 6$$ compared to $$f(x) = |x|$$?

Accepted Answer

Shift right 1, vertical stretch by 2, shift down 6

Question 10

If $$f(x) = -2x + 3$$ and $$g(x) = \frac{16}{x}$$, what is $$(f + g)(8)$$?

Accepted Answer

$$-1$$

Question 11

Given $$f(x) = 2x^2$ - 3x + 5$$, what is $$f(-4)$$?

Accepted Answer

$$53$$

Question 12

Which of the following is the correct simplification of $$(3 - 4i)(3 + 4i)$$?

Accepted Answer

$$25$$

Question 13

Find the linear function with slope $$m = -2$$ and $$f(0) = 8.$$

Accepted Answer

$$f(x) = -2x + 8$$

Question 14

Given $$f(x) = -2x^2$ + 3x$$ and $$g(x) = 4x + 2$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$-2(4x + 2)^2$ + 3(4x + 2)$$

Question 15

If $$f(x) = \frac{2x}{x-1}$$ and $$g(x) = \frac{3}{x+2}$$, what is the domain of $$f(x) + g(x)$$?

Accepted Answer

$$x 
eq 1, x 
eq -2$$

Question 16

Which of the following is the correct result of $$2(3 + 3i) - 4(2 - i)$$?

Accepted Answer

$$-2 + 10i$$

Question 17

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x^2$ - 9$$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$x 
eq 3, x 
eq -3$$

Question 18

Which of the following best describes the intervals where $$f(x) = 2x^2$ + 5x - 12 is $$increasing?

Accepted Answer

$$x \u003e -\frac{5}{4}$$

Question 19

If $$f(x) = -x^2$ - 6x - 9$$, what is the vertex of the parabola?

Accepted Answer

Precalculus Test 1 Review: Step-by-Step Guidance

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