Mathematics, 07.07.2021 22:00 ashiteru123

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

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Answer from: ppoooiyip1589

$\displaystyle \boxed{k = 3}$

Step-by-step explanation:

to determine the Value of k we need to find the equation of f(x) and g(x)

finding the equation of f(x):

f(x) is a linear function which form is given by:

$\displaystyle f(x) =mx + b$

where:

m is the slope b is the y-intercept

from the graph we acquire that

b = 4

to figure out m we can consider the following formula:

$\displaystyle m = \frac{ \Delta y}{ \Delta x}$

from the graph we obtain that both ∆x and ∆y is 1 thus substitute:

$\displaystyle m = \frac{ 1}{ 1}$

simplify:

$\displaystyle m = 1$

altogether we acquire:

$\displaystyle f(x) =x + 4$

finding the equation of g(x):

likewise f(x)

from the graph we obtain that

∆x=1∆y=3

thus substitute:

$\displaystyle m = \frac{ 3}{ 1}$

simplify:

$\displaystyle m = 3$

from the graph we acquire

b=4

altogether substitute therefore

$\displaystyle g(x) =3x + 4$

finding the value of k:

given that,

$\displaystyle \rm f(x) \: \text{and} \: g(x) =f(kx) = 3x + 4$

so our equation is

$\displaystyle kx + 4 = 3x + 4$

cancel 4 from both sides:

$\displaystyle kx = 3x$

divide both sides by x:

$\displaystyle \boxed{k = 3}$

and we're done!

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the complete question:

Answer from: goldwinner300

k = 3

Step-by-step explanation:

Graph is in attachment .

Finding equation of first line [ f(x) ] :-

We can see that the line passea through point ( 0,4) . Therefore ,

y intercept = 4

Also it passes through (-4,0 )

Now let's find out slope .So that we can use the slope intercept form to find the equⁿ of the line.

m = y ₂ - y₁ / x ₂ - x₁ m = 4 - 0 / 0 - (-4) m = 4/4 m = 1

Equation of f(x) :-

y = mx + c y = 1 * x + 4 y = x + 4 f(x) = x + 4

Similarly when we will find the equⁿ of g(x) :-

y = 3x + 4g(x) = 3x + 4

By question :-

f(x ) and g(x) = f ( k • x ) 3x + 4 = kx + 4 kx = 3x k = 3
Given f(x) and g(x)= f(k•x), use the graph to determine the value of k

Answer from: Quest

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Answer from: Quest

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