Exam 4/ Final Exam

Exam 1

100

Solve for the variable 

8(3 + ^) - 23a = a

a = 3

200

Simplify the expression 

√(20/125) 

2/5

300

Factor the perfect square trinomial 

32x² + 80x + 50 

2(4x+5)²

400

Simplify the expression without using the fractional exponents 

a^5/2√(32) - a^5/2√(18)

a²√(2a)

500

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a² + 1 / 2a

Exam 2

100

For the following exercise, find the domain of the function using interval notatiion

f(x) = -2x(x + 2)(x - 1)

(-oo, oo)

200

Find the equation of a line containing the following points. Write the equation in slope-intercept form.

( - 1, - 1) and ( - 2, - 4) 

y = 3x + 2 

300

Solve the equation.

|3x - 1| = 4 

x = -1, 5/3

400

For the following exercise, solve the equation. Use a substitute variable and find all real solutions by factoring.

(x² - 1)² + 2(x² - 1) - 15 = 0 

x = - 2, 2 

500

The cost of dollars of making x items is given by the function C(x) = 20x + 500 

Suppose the maximum cost allowed is $2500. What are the domain and range of the cost function C(x)? 

Domain: [0, 100]

Range : [500, 2500] 

Exam 3

100

Find f^-1(x) for the function

f(x) = x + 3 

f^-1(x) = x - 3

200

TRUE OR FALSE: The lines of the function are parallel 

3x + 3y = 12

y = -x 

TRUE

300

Solve by substitution 

x - 5y = 2

- 4x + 3y = 9 

(x , y) = (-3, -1) 

400

For the following exercise, write a function obtained when the graph is shifted as described 

f(x) = 1/x is shifted down 4 units and to the left 8 units 

(1 / (x + 8)) - 4

500

The indicated functions given 

f(x) = 2x² + 4 and g(x) = 3x - 3 

Find g(f(x)) 

g(f(x)) = 6x² + 9

Exam 4

100

Write 5^-9/10 in logarithmic form 

DNE 

200

Find the intercepts for the function 

g(x) = 3(x + 1)(x + 2)(x - 5)

x-intercepts: ( -2, 0), ( -1, 0), (5, 0)

y - intercepts : (0, -30) 

300

Find the vertical asymptote of the function

f(x) = log₂(15 - 5x) + 6 

VA : - 3 

400

Expand the expression

log((x¹⁵y¹³)/z¹⁹) 

15log(x) + 13log(y) - 19log(z) 

500

Solve the equation

2log(8n  + 4) + 6 = 10 

n = 12 

Exam 4

100

Rewrite the equation in exponential form

log_y(137) = x 

y^x = 137

200

State the domain and range of the function 

f(x) = ln(4x + 17) - 5 

Domain : (-17/4, oo) 

Range: (-oo, oo) 

300

Condense to a single logarithm 

log₃(2) + log₃(a) + log₃(11) + log₃(b) 

log₃22ab 

400

Solve the exponential equation 

4^{-3y -2} = 4^-y 

n = -1 

500

Solve for the equation 

ln(x) + ln(x - 3) = ln(7x) 

x = 10