Question

If g(x) is the f(x)=x after a vertical compression by 34 , a shift left by 3, and a shift down by 4,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

Answer:

a)

`g(x)=(3)/(4)(x+3)-4`

b) The slope of the line is 3/4

c) The vertical intercept -7/4

Step-by-step explanation:

The given function is:

f(x) = x

After a vertical compression by a factor of 3/4, we have:

`(3)/(4)x`

Then a shift to the left by 3

`(3)/(4)(x+3)`

Then a shift downwards by 4 to form g(x)

`g(x)=(3)/(4)(x+3)-4`

Write the equation above in the slope-intercept form

`\begin{gathered} g(x)=(3)/(4)x+(9)/(4)-4 \\ \\ g(x)=(3)/(4)x-(7)/(4) \end{gathered}`

Comparing the equation above with g(x) = mx + c

The slope, m = 3/4

The vertical intercept, c = -7/4