Question

Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k.

Answer 1

Answer:

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Answer 2

Given:

Given functions are: $f(x)$ and $g(x) = f(k.x)$.

Also, graph of the functions is also given.

To find:

We should find the value of $k$.

Solution:

Before solving the question, first we should find the equation of $f(x)$ and $g(x)$.

Finding the equation of $f(x)$,

If we observe the graph carefully,

The point of intersection of $f(x)$ and $x$-axis is at the point: $(-4,0)$

The point of intersection of $f(x)$ and $y$-axis is at the point: $(0,4)$

We know that, equation of a line is given by the formula,

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

So,

$\Rightarrow y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

$\Rightarrow y-0=\frac{4-0}{0-(-4)} (x-(-4))$

$\Rightarrow y=\frac{4}{4} (x+4)$

$\Rightarrow y=1(x+4)$

$\Rightarrow y=x+4$

But, $y=f(x)$.

So, equation is $f(x)=x+4$.

Now,

$g(x) = f( kx)$

$\Rightarrow g(x) = kx+4$

If we observe the given graph, the function $g(x)$ is passing through the point $(-2,-2)$.

So, $g(-2) = -2$

$\Rightarrow -2= k(-2)+4$

$\Rightarrow -2=-2k+4$

$\Rightarrow -2-4=-2k$

$\Rightarrow -6=-2k$

$\Rightarrow 3=k$

$\Rightarrow k=3$

Therefore, the value of $k$ is equal to 3.