Math 101 Unit 2 Homework
1. Graph. Indicate at least three points used for each graph. (4 pts)
a. x – 4y = 8
Three points used _________________
c. y = -1
Three points used _______________
b. x = 3
Three points used _________________
d. y = ⅓ x – 4
Three points used _____________
2. Let f(x)= 6x² + 5x –2
and g(x) = -2x + 5. Evaluate ( 2pts)
f (-2) ______________
g (3) _______________
3. The function f(x) = .81x + 168.3 models the cholesterol level of an American woman as a
function of her age x, in years. Use the function to find f(75). ( 1pt)
4. Find the x and y intercepts for the following. Write the intercepts as points. ( 4pts)
a. x + 3y = 9
x intercept _________
y intercept ____________
b.-6x = y - 4
x intercept __________
y intercept ____________
5. Find the slope of the line through the given points. ( 2pts)
a. (1,5) and (5,11)
b. (-7,4) and (-1,4)
6. Find the slope and y intercept of the following line. Rewrite the equation in slope intercept
form and write the intercept as a point. (2pts)
2x – 3y = 6 slope ____________
y intercept ____________
7. Solve the following system of equations using graphing. Indicate at least two points used to
graph each line in the space provided. (6 pts)
a. 3x – 2y = -3
-3x – y = -6
b. x + 2y = 6
2x + 4y = 8
3x – 2y = -3
x + 2y = 6
Points used ________________
Points used _________________
-3x – y = -6
2x + 4y = 8
Points used __________________
Points used _________________
Solution _____________
Solution ______________
8. Solve the following system of equations using substitution. All work must be shown with this
method to receive credit. ( 6 pts)
a. 7x – y = 32
2x + 3y = 19
c. 3x – y = 5
y = 3x – 5
b. 2x + 8y = 3
x + 4y = 8
9. Solve the following system of equations using elimination. All work must be shown with
this method to receive credit. ( 8 pts)
a. - x + 3y = 4
- 2x + 6y = 8
c. 7x + 4y = 7
6x + 7y = 31
b. 2x + 2y = 5
x+y=3
d. -2x – 4y = -1
5x + 10y = 15
10. Graph the system of linear inequalities. Indicate two points used for each line. (4 pts)
a. y ≥ 2x + 1
x+y≤3
b. y ≥ -4
x≥ 1
y ≥ 2x + 1
y ≥ -4
points used _________________
points used _____________
x+y≤3
x≥ 1
points used __________________
points used ______________
11. Given the following graph and objective function, find the maximum and minimum values of
the objective function and where it occurs. (2pts)
Objective Function
Z = 2x + 5y
Maximum Value ______________
occurs at x = ________________
Minimun Value ________________
occurs at x = ____________
12. Graph the following parabola and answer the questions. Be sure to write the intercepts as
points. (5pts)
f (x) = -x² + 4x – 3
Vertex ____________
X intercepts _____________
Y intercepts ______________
Three points used ______________
13. Create a scatter plot of the data and then determine if the data is best described by a linear,
exponential, logarithmic, or quadratic function. (4pts)
a. x
0.3
0.5
1
2
3
4
y
0.1
0.3
1
1.7
2.2
2.4
Model __________________
b.
x
y
0.1 0.3
1 0.5
1.7 1
2.5 2
3.5 4
3.2
3
Model ___________________