Inspect the graph below, which shows a function, f, and its transformation, g(x)=f(x+k). What is the value of k?
1.5 points
1.5
Question 2
2.
Let f(x)=120x-36 and h(x)=-\frac{5}{18}f(x).
A. What is the slope-intercept equation for h(x), (something like h(x)=mx+b)?
B. What is the slope of h(x)?
C. What is the y-intercept of h(x)?
1 point
1
Question 3
3.
Which equations match the graph?
1 point
1
Question 4
4.
If f(x)=8x-9 and g(x)=f(x-3), which equation defines g(x)?
1.5 points
1.5
Question 5
5.
A company that manufactures widgets has recently purchased a new widget-production machine. They expect the new machine to be able to produce 300 \frac{\textrm{widgets}}{\textrm{day}}. The company always sells 100 \frac{\textrm{widgets}}{\textrm{day}}. They also track the number of widgets they have in inventory by subtracting the number of widgets people have ordered from the number of widgets they physically have in stock. Their current inventory figure is -875 widgets.
The operations manager at the company determines that their inventory will be a function of the number of days they've been using the new machine. The function will be f(x)=200x-875, where x is the number of days they've been using the new machine, and f(x) is their net inventory.
Suppose the new machine underperforms its advertised capabilities and only produces 250 \frac{\textrm{widgets}}{\textrm{day}}.
A. Write a new function g(x) that determines net inventory as a function of the number of days the new machine has been in use.
B. Describe the transformation from f(x) to g(x).
C. Is the y-intercept of g(x) different from the y-intercept of f(x), or the same? In the context of the scenario, why does that make sense?
0 points
0
Question 6
6.
BONUS: Maximum 2 percentage points
Give the upper and lower bounds of the domain and range of the function g(x) from the scenario above.