Quiz 1 Solutions
Math 125
Allen Lab Section
Spring 2017
(1) (2.5 points) Given the function f (x) = x2 + x, completely simplify the expression
f (x + h) − f (x)
(x + h) − x
Solution:
f (x + h) − f (x)
(x + h)2 + (x + h) − (x2 + x)
=
(x + h) − x
x+h−x
2xh + h2 + h
x2 + 2xh + h2 + x + h − x2 − x
=
= 2x + h + 1
h
h
[1 point for plugging in values correctly, 1.5 points for simplifying completely]
=
(2) (2.5 points) Fully factor and simplify the following expression.
1
3
12(x + 3)2 (2x − 1)− 2 − 5(x + 3)3 (2x − 1)− 2
Solution:
(x + 3)2 (2x − 1)−3/2 (12(2x − 1) − 5(x + 3))
= (x + 3)2 (2x − 1)−3/2 (19x − 27)
[1.5 points for factoring out the correct quantities, 0.5 for the correct powers on factors,
and 1 point for quantity inside parenthesis. Either form was accepted on this quiz,
but on future assignments make sure you simplify completely, as shown in the last line
here.]
(3) (2.5 points) Suppose that the demand for Colins kidney pies is linear in the price P .
Determine the demand function N as a function of P giving the number of pies sold
when the price is P if he can sell 100 pies when the price is $5.00 and he can sell 40
pies when the price is $10.00.
60
100 − 40
=
= −12 is the slope of the
Solution: N (5) = 100 and N (10) = 40, so
5 − 10
−5
linear function. Using the form N (P ) = −12P + b, 100 = −12 ∗ 5 + b, and thus b = 160.
So, N (P ) = −12P + 160. [1 point for correct slope, 0.5 for form of linear equation,
1 point for y-intercept and final answer. Note that we were told in the problem this
function was linear, and that’s why we were able to solve this.]
(4) (2.5 points) Sketch the graph of the function
(
1
0<x<2
f (x) =
x 2
−(x − 3)
x≥2
Solution:
[1 point for each piece and 0.5 points for correct end behavior. If you would like to see
my sketched graph, come to office hours.]