UncategorizedCOLLEGE ALGEBRA

Hits: 0

1. 
2. (10 pts) For each function, yes or no: is the function symmetric with respect to the x-axis? The y-axis?
3. f(x) = 3x² – 4             x-axis_____________  y-axis ______________
4. f(x) = 3x – 4               x-axis ____________  y-axis ______________
5. f(x) = 3x³ x-axis ____________  y-axis ______________
6. f(x) = 3|x| – 4              x-axis ___________   y-axis ______________
7. f(x) = 3                        x-axis ___________   y-axis ______________
8. (5 pts) Let f(x) = |x| + 2
9. State the zero(s) of the function in ordered pair format.   ____________
10. State whether f(x) is even, odd, both, or neither          ____________
11. (5 pts) Let f(x) = -|x| + 1
12. State the zero(s) of the function in ordered pair format. ____________
13. State whether f(x) is even, odd, both, or neither              ____________
14. (5 pts) What do we mean by the term zero anyway?
15. (10 pts) Given the points (-2, 3) and (2, -3)
16. Find the point-slope equation of the line passing through the two given points. Show your work.

 

 

 

 

 

1. Find the slope-intercept equation of the line. Show your work.

 

 

 

 

 

6. (10 pts) Given the equation y = 4x + 5
7. Find the equation of the line parallel to y that passes through the point (1,2)

 

 

 

 

1. Find the equation of the line perpendicular to y that passes through the point (1,2)

 

 

 

 

 

7. (5 pts) What do we mean by the terms parallel and perpendicular, anyway?

 

 

8. (10 pts) The number of guests g in a water park t hours after 9 AM is given by the equation

g(t) = -10t² + 200t + 250    0 < t < 8      where t = 0 corresponds to 9 AM

1. Find the average rate of change of g over the interval [4, 7]  Remember to include the units

 

 

1. What times of the day does the interval [4, 7] represent?

 

1. State in English what your calculated answer from part a represents.

 

9. (10 pts) Rainbow wants to purchase custom-made pens to advertise her business. Two companies offer different design prices:

Company A: Pay a design fee of $75 plus $4.20 per pen

Company B: pay a design fee of $95 plus $3.80 per pen

1. Write the linear function c(x) that represents Company A’s total charge for x pens

 

1. Write the linear function c(x) that represents Company B’s total charge for x pens

 

1. For what number of pens is the total charge the same for both companies? Remember to include the units.

 

1. Rainbow wants to purchase 150 custom pens as cheaply as possible. With which company should she place the order? Show your work/explanation

 

10. (10 pts) Write the piece-wise function definition of f(x) shown in the graph.

 

Then state which graph (A, B, C, or D) represents the graph of y = f(x – 1) – 1 and why.  (The grids are supplied for scratch work; You are NOT required to submit your own graph)

        y = f (x)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

GRAPH A (below)                                     GRAPH B (below)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

GRAPH C (below)                                  GRAPH D (below)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11. (10 pts) Given the graph of the piecewise function y = f (x) pictured below:

 

 

• State the value of f (-1).

 

 

 

(b) State the x-intercept(s), if any, in ordered pair format.

 

 

 

(c) State the y-intercept(s), if any, in ordered pair format.

 

 

 

(d) State the domain of the piecewise function in interval notation.

 

 

 

(e) State the range of the piecewise function in interval notation.

 

 

 

(f) State the interval(s) on which the function is increasing. That is, for what x-values is the function increasing?

 

 

 

(g) State the interval(s) on which the function is decreasing. That is, for what x-values is the function decreasing?

 

12. (10 pts) Life expectancy at birth is the estimated lifespan of a baby born in a particular year (given the conditions of that time period).  Based on data retrieved from http://www.indexmundi.com/facts/united-states/life-expectancy-at-birth the following chart of U.S. life expectancy for males has been prepared.

The regression line is:

 

y = 0.2052x  – 336.5

 

where

 

x = birth year

 

and

 

y = U.S. life male expectancy, in years.

 

The value of r² is 0.9809.

 

1. Use the regression equation to estimate the U.S. life expectancy of a male baby born in 1969, to the nearest tenth of a year. Show your work.

 

 

 

 

 

1. Use the regression equation to predict the U.S. life expectancy of a male baby born in 2018, to the nearest tenth of a year. Show your work.

 

 

 

 

 

1. What is the slope of the regression line and what are the units of measurement?

 

 

 

 

 

1. In a sentence, interpret what the slope is telling us, in the context of this real-world application.

 

 

 

 

1. What is the value of the correlation coefficient, r? Also, interpret its value: Looking at the graph and the size of r, do you judge the strength of the linear relationship to be very strong, moderately strong, somewhat weak, or very weak?