Question

If g(x) is the f(x)=x after a vertical compression by 35 , a shift left by 2, and a shift up by 3,a) write an equation for g(x) : g(x) = b) The slope of this line is: c) The vertical intercept of this line is:

Answer 1

we have the parent function

f(x)=x

step 1

vertical compression by 3/5

so

x ---------> (3/5)x

step 2

shift left by 2

(3/5)x ------------> (3/5)(x+2)

step 3

shift up by 3

(3/5)(x+2) --------> (3/5)(x+2)+3

so

g(x)= (3/5)(x+2)+3

Part 2

The slope is 3/5

part 3

Vertical intercept

The y-intercept is the value of y when the value of x=0

For x=0

g(x)= (3/5)(0+2)+3

g(x)=(6/5)+3

g(x)=21/5

the y-intercept is the point (0,21/5)