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Mathematics 141 fifth homework
due Monday, January 27, 2014
show your work to get credit for each problem
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14. The graph of y = x is vertically
stretched by a factor of two, and then is
reflected across the x-axis. Write down the
equation of this new modified graph.
13. The graph of y = x3 is moved two
units to the right and then shifted down
five units. Write down the equation of this
new modified graph.
15. Find an equation for each graph sketched below:
y
y
half-parabola
2
2
x
-2
x
-3
y
2
1
x
1
parabola
16. Suppose that a city’s transit ridership x and the price per ride p are linearly related.
The transit ridership is two million when the fare is $2 per ride, while the ridership is only
1.75 million when the fare is $2.10.
• find the linear relation between x and p
• the total revenue from fares R = px. Write R as a function of p.
page two
17. A square-bottomed rectangular box with no top is to contain a volume of eight cubic
feet. Let x be equal to the length of a side of the square bottom, and let h be equal to the
height of the box. Write the surface area A of the box as a function of x.
18. Simplify the difference quotient
f (x + h) − f (x)
for the function f (x) = 5−3x .
h
19. Find a formula for a linear function F whose average rate of change is equal to 4/5 and
for which F (10) = 30.
20. Solve the absolute value inequality: |x − 53| < 3.