Write a rule for g

Question

Let the graph of g be a vertical stretch by a factor of 3, followed by a translation 2 units left of the graph of f(x) = 2 √(x) − 1.

Write a rule for g.

Answer 1

Hi Jordan,

When they say "let the graph of g be..." and then "write a rule for g", they are asking you to figure out g(x), which has the transformations from f(x) that the problem describes.

Starting with f(x):

f(x) = 2*√(x)-1

To make a vertical stretch by factor of 3, we want all of the y values to be multiplied by 3. The y values are = 2*√(x)-1, so we should multiply the coefficient 2 x 3 to make the vertical stretch.

(vertical shrink by 3, for example, would require dividing the coefficient 2 ÷ 3 to make a vertical shrink)

So we would have g(x) = 6*√(x)-1, but we also need to translate 2 units left.

To translate 2 units left, we need to go inside the parentheses of the square root, and have (x+2) instead of just (x). Adding 2 to x inside the parentheses will translate 2 units left.

(subtracting 2 inside the parentheses would translate 2 units right)

So, the answer is g(x) = 6*√(x+2)-1

Hope this helps. :)