Question

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

Answer 1

Answer:

Option A k=5

Step-by-step explanation:

step 1

Find the equation of f(x)

we have the points

(-10,-6) and (0,4)

Find the slope m

$m=(4+6)/(0+10)=1$

The function in slope intercept form is equal to

$f(x)=mx+b$

we have

$m=1$

$b=4$ -----> the point (0,4) is the y-intercept

substitute

$f(x)=x+4$

step 2

Find the equation of g(x)

we have the points

(-2,-6) and (0,4)

Find the slope m

$m=(4+6)/(0+2)=5$

The function in slope intercept form is equal to

$g(x)=mx+b$

we have

$m=5$

$b=4$ -----> the point (0,4) is the y-intercept

substitute

$g(x)=5x+4$

step 3

Find the value of k

we have

$f(x)=x+4$

$g(x)=5x+4$ -----> equation A

$g(x)=f(kx)$ -----> equation B

$f(kx)=kx+4$ ----> equation C

substitute equation A and equation C in equation B and solve for k

$kx+4=5x+4$

$kx-5x=0\\kx=5x\\k=5$