Question 1

Which of the following is the correct vertex for the parabola shown in the first image?

Accepted Answer

($$-1$$, $$-4)$$

Question 2

What is the domain of the function $$f(x) = \sqrt{2x + 5}$$?

Accepted Answer

$$\{x|x \geq -\frac{5}{2}\}$$

Question 3

Given the function $$f(x) = |x - 1| + 3$$, what is the range of $$f$$?

Accepted Answer

$$[3, \infty)$$

Question 4

Solve the inequality $$5 \u003e 3 - x \geq -1$$ and express your answer in interval notation.

Accepted Answer

$$(-2, 4]$$

Question 5

Which of the following functions has a vertical asymptote at $$x = 2$$?

Accepted Answer

$$g(x) = \frac{1}{(x - 2)^2$}$$

Question 6

If a beam of height 1 foot can support 4 tons, what is the maximum weight a beam of height 1.5 feet can support, given the weight varies directly as the square of its height?

Accepted Answer

9 tons

Question 7

What is the solution to the equation $$x^2 = 2x - 2$?

Accepted Answer

$$x = 1 \pm i$$

Question 8

Which of the following is the correct interval(s) of increase for the function graphed in the first image?

Accepted Answer

$$[-1, \infty)$$

Question 9

For the function $$f(x) = -x^2$ - 2x - 5$$, what is the vertex?

Accepted Answer

$$(-1, -4)$$

Question 10

What is the inverse of the function $$f(x) = 1 - \frac{1}{x}$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{1}{1 - x}$$

Question 11

Which of the following best describes the discriminant of a quadratic function whose vertex lies on the x-axis and opens upward?

Accepted Answer

The discriminant is zero.

Question 12

Given the function $$f(x) = 2x^2$ - 10$$, what are the x-intercepts?

Accepted Answer

$$(-\sqrt{5}, 0)$$ and $$(\sqrt{5}, 0)$$

Question 13

Which of the following is the correct simplified form of $$\ln(x-1) - 2\ln x + \ln 2x$$?

Accepted Answer

$$\ln\left(\frac{2(x-1)}{x^2$}\right)$$

Question 14

If you invest $$4000 at an $$annual interest rate of $$6.6\%$$ compounded continuously, how much money will you have after $$12$$ years?

Accepted Answer

$$8831$$

Question 15

Which of the following graphs represents a function?

Accepted Answer

The graph in image 5

Question 16

For the function $$g(x) = 2x^4$ - 512$$, what is the complete factorization?

Accepted Answer

$$2(x + 4)(x - 4)(x^2$ + 16)$$

Question 17

What is the symbolic representation of the function for the data: $$x = -1, 0, 1, 2, 3$$ and $$f(x) = 80, 40, 20, 10, 5$$?

Accepted Answer

$$f(x) = 80 \cdot (0.5)^x$$

Question 18

For the function $$h(x) = -1.2x^2$ + 4x + 35$$ describing a diver's trajectory, what is the maximum height reached?

Accepted Answer

$$38.33$$ feet

Question 19

What is the domain of $$h(x) = \log(-x + 5)$$?

Accepted Answer

$$\{x|x \u003c 5\}$$

College Algebra Final Exam Review – Step-by-Step Guidance

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