Q: For $$f(x) = \frac{3}{2x-5}$$, what is the domain?

$$\{x \mid x \neq \frac{5}{2}\}$$

Question 1

Solve the inequality $$8x + 3 \u003e 1$$ and express the solution in interval notation.

Accepted Answer

$$(\frac{1}{4}, \infty)$$

Question 2

A school has $$500 to spend on webcams, each costing 32.99. $$Which inequality represents the maximum number of webcams $$x$$ that can be purchased, and what is the greatest integer value of $$x$$?

Accepted Answer

$$32.99x \leq 500$$, $$x = 15$$

Question 3

Solve the quadratic equation $$x^2 - 4x - 12 = 0$ by factoring.

Accepted Answer

$$x = -6, x = 2$$

Question 4

Given the quadratic function $$f(x) = x^2$ + 6x - 4$$, what are the coordinates of the vertex?

Accepted Answer

$$(-3, -13)$$

Question 5

A projectile is launched with height $$h(t) = -4.9t^2$ + 229t + 234. $$What is the maximum height the projectile attains (rounded to the nearest meter)?

Accepted Answer

$$2679$$ meters

Question 6

For the function $$f(x) = \sqrt{2x - 3}$$, what is the domain?

Accepted Answer

$$[\frac{3}{2}, \infty)$$

Question 7

Given the graph of $$y = x^2$ + 6x - 4$$, which of the following statements is true?

Accepted Answer

The parabola opens upward, has a minimum at $$x = -3$$, and the axis of symmetry is $$x = -3.$$

Question 8

A vendor's weekly profit is given by $$f(x) = 18x - 0.15x^2$, where x$ is the number of boxes sold. How many boxes should be sold to maximize profit?

Accepted Answer

$$x = 60$$

Question 9

A farmer has 132 feet of fencing to enclose a rectangular area against a wall (see diagram). What dimensions maximize the area?

Accepted Answer

Width $$= 33 ft$$, Length $$= 66 ft$$

Question 10

Solve using the quadratic formula: $$x^2 = 8x - 9$.

Accepted Answer

$$x = 4 \pm 5$$

Question 11

Evaluate $$(f \circ g)(2)$$ for $$f(x) = \sqrt{x+1} - 3$$ and $$g(x) = x^2$ - 4.$$

Accepted Answer

$$-1$$

Question 12

For the piecewise function $$f(x) = \begin{cases} -4 & x \u003c 1 \ -2x + 1 & x \geq 1 \end{cases}$$, what is $$f(4)$$?

Accepted Answer

$$-7$$

Question 13

For $$f(x) = 3x - 8$$ and $$g(x) = x^2$, what is (f + g)(x$$)$$?

Accepted Answer

$$x^2 + 3x - 8$

Question 14

Solve the compound inequality $$-8 \u003c 2x + 6 \leq 20$$ and express the solution in interval notation.

Accepted Answer

$$(-7, 7]$$

Question 15

What is the range of the function $$f(x) = 2(x-3)^2$ + 1$$?

Accepted Answer

$$[1, \infty)$$

Question 16

For $$f(x) = \frac{3}{2x-5}$$, what is the domain?

Accepted Answer

$$\{x \mid x 
eq \frac{5}{2}\}$$

College Algebra Practice Problems – Step-by-Step Guidance

Guida di studio - Domande di pratica

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