Q: Describe the end behavior of $$f(x) = -4x^7$ + 3x^2$ - 1.$$

$$x \to \infty, f(x) \to -\infty; \ x \to -\infty, f(x) \to \infty$$

Question 1

Given the function $$g(x) = 8x - 3$$, what is the value of $$g(4)$$?

Accepted Answer

$$g(4) = 29$$

Question 2

Given the table below, what is the average rate of change of the function on the interval $$[-2, 2]$$?

x | y
---|---
-2 | -7
-1 | -4
0 | -1
1 | 2
2 | 5

Accepted Answer

$$\frac{5 - (-7)}{2 - (-2)} = 3$$

Question 3

Given $$g(x) = \frac{-x^2$}{x-2}$$, evaluate and simplify the difference quotient $$\frac{g(4+h) - g(4)}{h}.$$

Accepted Answer

$$-\frac{8+h}{6+h}$$

Question 4

Find the domain of the function $$f(x) = \frac{x-3}{2x^2$ - 7x + 3} in $$interval notation.

Accepted Answer

$$(-\infty, \frac{1}{2}) \cup (3, \infty)$$

Question 5

Given the graph below, what is the interval where the function is increasing?

Accepted Answer

$$(-\infty, -2) \cup (1, \infty)$$

Question 6

Given $$f(x) = 2x^7$ - 4x^3$ - 6x$$, determine if the function is even, odd, or neither.

Accepted Answer

Odd

Question 7

Let $$f(x) = \frac{4x-3}{3x+1}. $$Find the inverse function $$f^{-1}(x$$)$$.

Accepted Answer

$$f^{-1}(x$$) = \frac{x+3}{4-3x}$$

Question 8

A line passes through the points $$(-3, 4)$$ and $$(1, -2). $$What is the equation of a perpendicular line passing through $$(-6, -5)$$?

Accepted Answer

$$y + 5 = \frac{1}{3}(x + 6)$$

Question 9

Solve for $$t$$: $$4t + 2t^2$ + 6 = 7.$$

Accepted Answer

$$t = -3, \ t = \frac{1}{2}$$

Question 10

A rancher has 900 ft of fencing to enclose a rectangular area and divide it into five pens with fencing parallel to one side. What dimensions maximize the total area?

Accepted Answer

$$x = 150, \ y = 150$$

Question 11

Write the equation of the quadratic function with vertex at $$(2, -3)$$ and passing through $$(0, 1) in $$vertex form.

Accepted Answer

$$y = a(x-2)^2$ - 3$$, \ a = 1$

Question 12

Given $$P(x) is a $$degree 6 polynomial with a root of multiplicity 2 at $$x=1$$, and roots of multiplicity 1 at $$x=0$$ and $$x=-1$$, and passes through $$(2, 636)$$, what is the leading coefficient?

Accepted Answer

$$a = 6$$

Question 13

Describe the end behavior of $$f(x) = -4x^7$ + 3x^2$ - 1.$$

Accepted Answer

$$x 	o \infty, f(x) 	o -\infty; \ x 	o -\infty, f(x) 	o \infty$$

Question 14

Solve for $$x$$: $$2\log_5$ x + \log_5$ 10 - \log_5$(x+3) = 1.$$

Accepted Answer

$$x = 5$$

Question 15

Find the partial fraction decomposition of $$\frac{19x+9}{10x^2$+17x+3}.$$

Accepted Answer

$$\frac{2}{2x+3} + \frac{5}{5x+1}$$

Question 16

Determine the type of conic section represented by $$9x^2$$ - $$16y^2 - 36x - 32y - 124 = 0$ and find the center.

Accepted Answer

Hyperbola, center at $$(2, -1)$$

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