The function f(x)=2^x and g(x)=f(x+k). if k= -5, what can be concluded about the graph of g(x)?

the graph of g(x) is shifted vertically
a. 5 units above the graph of f(x)
b. 5 units below the graph of f(x)
c. the graph is not shifted vertically from the graph of f(x)

the graph of g(x) is shifted horizontally
a. 5 units to the left of the graph of f(x)
b. 5 units to the right of the graph of f(x)
c. the graph is not shifted horizontally from the graph of f(x)

The graph of g(x) is shifted horizontally  5 units to the right of the graph of f(x).

Step-by-step explanation:

Given :The function f(x)= and g(x)=f(x+k). If k= -5,

To find : what can be concluded about the graph of g(x).

Solution : The function parent f(x) = .

By the Transformation rule if f(x) transformed to f(x+k) it would shifted horizontally toward left by k units .

Then ,

g(x)=f(x+ (-5)) would be b. 5 units to the right of the graph of f(x).

Therefore, The graph of g(x) is shifted horizontally  5 units to the right of the graph of f(x).

d

step-by-step explanation:

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x