004 Sample Final A

This is a sample final, and is meant to represent the material usually covered in Math 8A. Moreover, it contains enough questions to represent a three hour test. An actual test may or may not be similar. Click on the boxed problem numbers to go to a solution.

Question 1

Find $f^{-1}(x)$ for $f(x)={\frac {3x-1}{4x+2}}$

Question 2

a) Find the vertex, standard graphing form, and x-intercepts for $f(x)={\frac {1}{3}}x^{2}+2x-3$
b) Sketch the graph. Provide the y-intercept.

Question 3

Solve. Provide your solution in interval notation. $\vert 4x+7\vert \geq 5$

Question 4

Graph the system of inequalities. $y>2x-3\qquad y\leq 4-x^{2}$

Question 5

Describe how the graph of $f(x)=3^{(x+1)}-2$ can be obtained from a basic graph. Then sketch the graph. Provide at least two ordered pairs, and the equation of any asymptote.

Question 6

Simplify. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3x + 6} - \frac{x}{x^2-4} + \frac{3}{x-2}}

Question 7

Given a sequence Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10, 7, 4, 1, \ldots} use formulae on the back page to compute $S_{20}$

Question 8

a) List all the possible rational zeros of the function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=x^4-4x^3-7x^2+34x-24} .
b) Find all the zeros, that is, solve Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = 0}

Question 9

Graph the function. Give equations of any asymptotes, and list any intercepts. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = \frac{6}{x^2 - x - 2}}

Question 10

Decompose into separate partial fractions. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{6x^2 + 27x + 31}{(x + 3)^2(x-1)}}

Question 11

Find and simplify the difference quotient Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{f(x + h) - f(x)}{h}} for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = \sqrt{x - 3}}

Question 12

Set up, but do not solve the following word problem. Two private airplanes travel toward each other from cities that are 780 km apart at speeds of 190 km/hr and 200 km/hr. They left at the same time. In how many hours will they meet?

Question 13

Compute Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \displaystyle{\sum_{n = 1}^6 4\left(\frac{1}{2}\right)^n}}

Question 14

a) Find an equation of the line passing through Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (-4, 2)} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (3, 6)} .
b) Find the slope of any line perpendicular to your answer from a)

Question 15

Solve. $\log(x+8)+\log(x-1)=1$

Question 16

Solve. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{x - 3} + 5 = x}