Q:

# The function f(x)=3g(x). Which of the following shows possible graphs of f(x) and g(x)?

Accepted Solution

A:
Answer:The answer is the first graph in the second rawStep-by-step explanation:* Lets study the dilation:- A vertical stretching is the stretching of the graph away  from the x-axis - A vertical compression is the squeezing of the graph  toward the x-axis. - if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically  stretched by multiplying each y-coordinates by k. - if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed  by multiplying each y-coordinates by k. * Notice that the "roots" on the graph stay in their same  positions on the x-axis. * Lets check our question:∵ f(x) = 3g(x) ∵ f(x) = k.g(x)∴ It is a vertical stretching or vertical compression∵ k = 3 > 1∴ It is vertical stretching with scale factor = 3* That means we will multiply each y-coordinates in g(x) by 3∴ The graph of f(x) will be away from x- axis and narrow to y- axis∴ The answer is the first graph the second raw Example: If g(x) = x²                 ∴ f(x) = 3x²* Look to the graph:- The red is the graph of g(x)- The blue is the graph of f(x)- f(x) = 3g(x)