1. Answer the undermentioned questions using the graph of f below.
a) Find f ( 4 ) . b) State the range of f using subdue set-builder or interval notation. c) Find any x-value for which f ( x ) = ?1 .
2.
Let f ( x ) = x 2 ? 2 and g ( x ) = 3 ? x . Find and simplify the following. a)
f (3 p ) =
b)
( f ? g )( x ) =
c)
( f ? g )( ?2 ) =
3.
Find the domain of apiece belong below. Be sure to state your process using appropriate set-builder or interval notation. a)
f ( x) = 3x + 1 x ? 3x + 2
2
b)
h ( x ) = 13 ? 6 x
4.
The ordnance gasoline mileage of a specific political machine is a linear function of the induce at which the car is driven. If the car is driven at a rate of 30 mph, the cars gas mileage is 35 miles per gallon. If the car is driven at 60 mph, the cars gas mileage is 20 miles per gallon.
a) Use this randomness to write the gas mileage, m ( s ) , as a function of the rush, s . b) Use your function to determine the gas mileage if the car is driven at a speed of 50 mph. Answer in a sentence.
5.
Perform the indicated operation. simplify your answer as much as possible.
a) b) c)
y2 + 4 y + 4 3y + 3 ? = y +1 y+2
x x4 ÷ = x2 ?1 x + 1 t2 8t ? 15 ? = t ?3 t ?3
d) e)
8 2r + = r ?5 5?r x 3 + = 2 x + 9 x + 20 x + 5
6.
Ellen and Doug have to clean their place. When Ellen does it by herself, it takes 7 hours. When Ellen and Doug work together, it takes 4 hours. How long would it take Doug to clean the house by himself? To get full credit, you must define your variant in words, write and solve a rational equation, and answer the question in a complete sentence.
7.
Solve each equation. If no solution exists, write no solution. 3 a + 11 a) = a +8 a +8 10 b) x + = 7 x 7 3 5 c) + = 2 2x x +1 2x + 2x
8.
Solve each peremptory value equation or inequality. Express your answers in setbuilder or interval notation.
a) b) c)
5x + 2 = 7
a+5 ? 3
4y ?5 < 7
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