Question

100 points!!!!!! PLEASE I NEED AN ANSWER ASAP

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Function g is shown on the graph. If function f is the parent linear function, f(x) = x, what is the equation of transformed function g in terms of f?

Answer 1

Answer:

$\mathsf {g(x) = \frac{1}{2} f(x)}$

Step-by-step explanation:

$\textsf {Given :}$

$\implies\textsf {f(x) = x}\\\implies \textsf {Graph of g(x)}$

$\textsf {Now we see from the equation and the graph}\\ \textsf {that both of them passes through the origin,} \\\textsf {hence they have both the x and y intercepts as 0.}$

$\textsf {Take any 2 points on g(x), like (0,0) and (2, 1) and find the slope.}$

$\implies \mathsf {m = 1 - 0 / 2 - 0}$

$\implies \mathsf {m = 1/2}$

$\textsf {Hence, equation of g(x) :}$

$\implies \mathsf {g(x) = 1/2x}$

∴ $\mathsf {But, f(x) = x}$

$\textsf {Therefore, g(x) in terms of f(x) is :}$

$\implies \mathsf{g(x) = \frac{1}{2} f(x)}$

Answer 2

Parent function.

• y=x

Now

for y=x

Find f(2)

• It's 1

The scale factor

• 1/2

Now final equation

• g(x)=1/2x
• g(x)=1/2f(x)

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