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)

$g(x)=\frac{3}{4}(x+3)-4$

b) The slope of the line is 3/4

c) The vertical intercept -7/4

Explanation:

The given function is:

f(x) = x

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

$\frac{3}{4}x$

Then a shift to the left by 3

$\frac{3}{4}(x+3)$

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

$g(x)=\frac{3}{4}(x+3)-4$

Write the equation above in the slope-intercept form

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

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

The slope, m = 3/4

The vertical intercept, c = -7/4