Question

2. If g(x) is a horizontal stretch by a factor of3 followed by a translation of 5 units up offx)=-7x +9, what is the rule for g(x)?F g(x)=-21x + 14G g(x)=-7x + 14H g(x)=-7/3x + 4. J g(x)=-7/3x+14

Answer 1

To stretch a function f(x) horizontally by a factor c we have to follow the rule:

`y=f((x)/(c))`

So, in this case, the function f(x) stretch by a factor of 3 woulb be:

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

To translate up a function f(x) by c units, we have to follow the rule:

`y=f(x)+c`

Applying this to our function y, and renaming it g(x), we have

`\begin{gathered} g(x)=-(7)/(3)x+9+5 \\ =-(7)/(3)x+14 \end{gathered}`

So our function g(x) will be

`g(x)=-(7)/(3)x+14`