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Lori graphed f(x) = −34x − 1 and g(x) = −4f(x) on the same coordinate plane. Which statements below incorrectly describe how the graphs of f(x)and g(x)are related?

Select all the correct answers.

A.The graph of f(x) is less steep than the graph of g(x).
B.The y-intercept of f(x) is 5 units above the y-intercept of g(x).
C.The graph of f(x) is shifted 4 units up to create the graph of g(x).
D.The y-intercept of f(x) is 3 units below the y-intercept of g(x).
E.The graph of f(x) has the same x-intercept as the graph of g(x).
F.The graph of f(x) is more steep than the graph of g(x).

Respuesta :

MrRoyal

The true statement about f(x) and g(x) is (a) the graph of f(x) is less steep than the graph of g(x).

The equations are given as:

[tex]f(x) = -\frac 34x -1[/tex]

[tex]g(x) = -4f(x)[/tex]

Substitute [tex]f(x) = -\frac 34x -1[/tex] in [tex]g(x) = -4f(x)[/tex]

[tex]g(x) = -4(-\frac 34x -1)[/tex]

Expand

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

So, the equations of f(x) and g(x) are:

[tex]f(x) = -\frac 34x -1[/tex]

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

A linear equation y = mx + b has a slope of m and a y-intercept of b.

So, the slopes of g(x) and f(x) are 3 and -3/4.

So, the y-intercept of g(x) and f(x) are 4 and -1

This means that

  • The graph of f(x) is less steep; option (a) is true
  • The y-intercept of f(x) is 5 less the y-intercept of g(x); option (b) is false

Both graphs are not the same, and they have different x-intercepts.

Hence, the true statement is (a)

Read more about linear functions at:

https://brainly.com/question/15602982

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