Please answer abcde and f of the question Let fx 2ex 1 Whi

Please answer a,b,c,d,e and f of the question.

Let f(x) = 2e^-x + 1. Which describes how the graph of f can be obtained from the graph of y = e^x ? Choice: Shift the graph of y = e^x to the left by 1 unit and shift upward by 1 unit. Shift the graph of y = e^x to the right by 1 unit, stretch vertically by a factor of 2, and shift upward by 1 unit. Reflect the graph of y = e^x across the x-axis. stretch vertically by a factor of 2, and shift upward by 1 unit. Reflect the graph of y = e^x across the y-axis, stretch vertically by a factor of 2, and shift upward by 1 unit. What is the domain of f ? What is the range of f ? What is the y-intercept ? What is the horizontal asymptote? Which is the graph of f?

Solution

f(x) = 2e^-x + 1

a) reflect the graph of e^x across y axis it becomes e^-x , stretch vertically by a factor of 2 it becomes 2e^-x and shift 1 unit upwards and it becomes 2e^-x + 1

(option d)

b) domain is all values of x where function exists

so here domain is all real values of x ( -infinity , + infinity )

c) range is all values of y where functions exists

range is y > 1 that is ( 1 to infinity )

d) y intercept

plug x =0 in the function

y = 2e^0 + 1 = 3

y intercept = (0,3)

e) horizontal asymptote is y = 1

f) graph c is correct option