Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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

Sagot :

Nayefx

Answer:

[tex] \displaystyle \boxed{k = 3}[/tex]

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:

[tex] \displaystyle f(x) =mx + b[/tex]

where:

  • m is the slope
  • b is the y-intercept

from the graph we acquire that

[tex]b = 4[/tex]

to figure out m we can consider the following formula:

[tex] \displaystyle m = \frac{ \Delta y}{ \Delta x} [/tex]

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

[tex] \displaystyle m = \frac{ 1}{ 1} [/tex]

simplify:

[tex] \displaystyle m = 1[/tex]

altogether we acquire:

[tex] \displaystyle f(x) =x + 4[/tex]

finding the equation of g(x):

likewise f(x)

from the graph we obtain that

  • ∆x=1
  • ∆y=3

thus substitute:

[tex] \displaystyle m = \frac{ 3}{ 1} [/tex]

simplify:

[tex] \displaystyle m = 3[/tex]

from the graph we acquire

  • b=4

altogether substitute therefore

[tex] \displaystyle g(x) =3x + 4[/tex]

finding the value of k:

given that,

[tex] \displaystyle \rm f(x) \: \text{and} \: g(x) =f(kx) = 3x + 4[/tex]

so our equation is

[tex] \displaystyle kx + 4 = 3x + 4[/tex]

cancel 4 from both sides:

[tex] \displaystyle kx = 3x [/tex]

divide both sides by x:

[tex] \displaystyle \boxed{k = 3}[/tex]

and we're done!

Disclaimer:

at the following link we posted the complete question

the complete question:

  • https://brainly.com/question/24201282
VirαtKσhli

Answer:

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 + 4
  • g(x) = 3x + 4

By question :-

  • f(x ) and g(x) = f ( k • x )
  • 3x + 4 = kx + 4
  • kx = 3x
  • k = 3
View image VirαtKσhli
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.