5 Problems - SHOW ALL WORK!
1. Write a function that describes the cost to have your vehicle towed if you are charged $15 for the pickup plus $2 for every mile.
2. The cost of a gym membership if there is a $50 enrollment fee and the charge is $35 a month.
3. Use the following functions to solve each:
f(x)= 2x - 3 g(x)= -4x -1
What is f(3)?
Which function has a steeper slope?
4. Use the following functions to solve each:
f(x) = 2x -3 4x - 7y = 28
Which function has the greater y-intercept?
What is f(-2)?
5.
A. Does the table or the graph represent a steeper slope?
B. Does the table or the graph have a bigger y-intercept?
1. The function to describe the cost of towing a vehicle is:
Cost = $15 + $2/mile
2. The cost of a gym membership is:
Cost = $50 (enrollment fee) + $35/month
3. To find f(3), substitute x = 3 into the formula for f(x):
f(3) = 2(3) - 3
f(3) = 6 - 3
f(3) = 3
To determine which function has a steeper slope, compare the coefficients of x in f(x) and g(x). The coefficient in front of x in f(x) is 2, while the coefficient in front of x in g(x) is -4. Since -4 is greater than 2, g(x) has a steeper slope.
4. To compare the y-intercepts of f(x) = 2x - 3 and 4x - 7y = 28, we need to rewrite the second equation in slope-intercept form:
4x - 7y = 28
-7y = -4x + 28
y = (4/7)x - 4
Comparing the y-intercepts, we can see that f(x) = 2x - 3 has a y-intercept of -3, while the line y = (4/7)x - 4 has a y-intercept of -4. Therefore, f(x) = 2x - 3 has the greater y-intercept.
To find f(-2), substitute x = -2 into the formula for f(x):
f(-2) = 2(-2) - 3
f(-2) = -4 - 3
f(-2) = -7
5.
A. To determine if the table or the graph represents a steeper slope, compare the rates of change between any two points on the table or the graph. The one with a greater rate of change has a steeper slope.
B. To determine if the table or the graph has a bigger y-intercept, compare the values of the y-coordinate when x = 0 for both the table and the graph. The one with the larger y-coordinate has a bigger y-intercept.