Question

Diana is a piano teacher who charges $45 per hour plus an additional flat fee of $20 for travel. The equation that represents this situation is y = 45x + 20, where x represents the number of lesson hours, and y represents the total cost. Another piano teacher, Paula, creates a graph to compare the total amount Diana charges with the total amount she charges for lessons. Paula observes that the graph of her function looks the same as the graph of Diana's function except that it is shifted 2 units below it. Select the function that represents the total amount Paula charges. A. f(x) = 43x + 20 B. f(x) = 45x + 18 C. f(x) = 43x + 18 D. f(x) = 45x + 22

Answer 1

To shift vertically the graph of the function $f(x)$, you have to add a constant to its expression:

$f(x) \to f(x)+k$

If k is positive, you shift the function k units above, if k in negative, you shift the function k units below.

So, if you want to shift the graph of $f(x)=45x+20$ two units down, you have to subtract 2 (i.e., add -2):

$f(x) = 45x+20 \to 45x+20-2 = 45x+18$