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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

Respuesta :

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

[tex]y=f(\frac{x}{c})[/tex]

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

[tex]\begin{gathered} y=-7(\frac{x}{3})+9 \\ =-\frac{7}{3}x+9 \end{gathered}[/tex]

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

[tex]y=f(x)+c[/tex]

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

[tex]\begin{gathered} g(x)=-\frac{7}{3}x+9+5 \\ =-\frac{7}{3}x+14 \end{gathered}[/tex]

So our function g(x) will be

[tex]g(x)=-\frac{7}{3}x+14[/tex]

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