College Algebra Exam #1
Fall 2013
Name __________________________________
Make sure you show all of your work neatly on this paper. Solutions without correct supporting work will not earn
credit, even if they are correct. All answers must be exact unless the problem specifically says to round.
1. Find an equation of the line containing the given pair of points:
Write your answer in slope-intercept form. (8 points)
(3,1) and (9,4)
2. Write a slope-intercept equation for a line passing through the given point that is parallel to the given line.
(3, -6); 4𝑥 + 9𝑦 = 8
(8 points)
3. Find the domain of the functions. Circle your answers. (8 points each)
a. 𝑔(𝑥) =
𝑥
𝑥 2 +8𝑥+7
b. 𝑓(𝑥) = √2𝑥 − 5
4. For the function 𝑓(𝑥) = 3𝑥 2 − 1, construct and simplify the difference quotient
(8 points)
𝑓(𝑥+ℎ)−𝑓(𝑥)
ℎ
.
5. Find (𝑓 ∘ 𝑔)(𝑥) for 𝑓(𝑥) = 3𝑥 2 + 6 and 𝑔(𝑥) = 5𝑥 − 5.
(8 points)
6. Write an equation for a function that has a graph with the shape of 𝑦 = 𝑥 2 , but upside-down, shifted up 3 units, and
shifted right 6 units.
(8 points)
7. Fit a regression line to the data shown in the chart, and find the coefficient of correlation for the line. Use the
regression line to predict life expectancy in the year 2012.
Year, x
0 (1990)
2 (1920)
4 (1940)
6(1960)
8 (1980)
Life expectancy, y 48.7 years 51.0 years 52.6 years 53.8 years 54.8 years
a.
Write the equation of the regression line. Round to 3 decimal places.
(5 points)
b.
The coefficient of correlation rounded to 3 decimal places is ________________.
(2 points)
c. The life expectancy in the year 2012, rounded to one decimal place is _______________. (3 points)
8. Graph by hand. Show your t-chart(s).
 x 2  2, x  1
f ( x)  
2 x  3, x  1
(8 points)
9. A kayak moves at a rate of 10 mph in still water. If the river’s current flows at a rate of 4 mph, how long does it take
the boat to travel 36 mi upstream? Round your answer to the nearest tenth of an hour. You must clearly state what
your variables represent and set up a mathematical equation that represents the problem to earn credit.
(8 points)
10.
Use the graph of y=f(x) given below to answer the questions.
Domain: ______________________ (2 points)
Range: __________________________ (2 points)
Interval(s) where f is idecreasing: ____________________________ (2 points)
Graph 𝑦 = 𝑓(𝑥 − 2) + 3 on the same coordinate system given above.
11.
Solve and write your answer using interval notation:
2
3
4
(4 points)
≤ − 5 (𝑥 − 3) < 1
(4 points)
12. Graph the function f(x) = 1.9x4 – 4.8x2 + 3.19 on the window [–4, 4, –8, 8]. Then find any relative maxima or
minima.
(4 points)