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Consider the function,

f(1) = 21 - 6

Match each transformation of Rx) with its description.

g() = 21 – 10

9(0) = 21 - 14

g(1) = 81 - 4

g(t) = 21 - 2

g(1) = 81 - 24

g(I) = 85 - 6

shifts 1x) 4 units right

stretches x) by a factor

of 4 away from the x-axis

compresses (x) by a factor

of 4 toward the y-axis

shifts x 4 units down

Respuesta :

MrRoyal

Answer:

Shift 4 units down: [tex]g(x) = 2x - 10[/tex]

Stretching f(x) by 4 : [tex]g(x) =8x - 24[/tex]

Shift 4 units left:  [tex]g(x) = 2x - 14[/tex]

Compress by 1/4 units : [tex]g(x) = 8x - 6[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 2x - 6[/tex]

Required

Match the transformations (See attachment)

Shift 4 units down

Shifting down a function is represented as:

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

In this case:

[tex]b = 4[/tex]

Substitute expression for f(x) and 4 for b in [tex]g(x) = f(x) - b[/tex]

[tex]g(x) = 2x - 6 - 4[/tex]

[tex]g(x) = 2x - 10[/tex]

Stretching f(x) by 4

Stretching a function by some units is represented as:

[tex]g(x) =b.f(x)[/tex]

In this case:

[tex]b = 4[/tex]

Substitute expression for f(x) and 4 for b in [tex]g(x) =b.f(x)[/tex]

[tex]g(x) =4 * (2x - 6)[/tex]

[tex]g(x) =8x - 24[/tex]

Shift 4 units left

Shifting a function to the left is represented as:

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

In this case:

[tex]b = 4[/tex]

Substitute expression for f(x) and 4 for b in [tex]g(x) = f(x - b)[/tex]

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

Calculating f(x - 4)

[tex]f(x) = 2x - 6[/tex]

[tex]f(x - 4) = 2(x - 4) - 6[/tex]

[tex]f(x - 4) = 2x - 8 - 6[/tex]

[tex]f(x - 4) = 2x - 14[/tex]

Hence:

[tex]g(x) = 2x - 14[/tex]

Compress by 1/4 units

This means that the function is stretched by [tex]1/\frac{1}{4}[/tex]

Compressing a function is represented as:

[tex]g(x) =f(bx)[/tex]

In this case:

[tex]b = 1/\frac{1}{4}[/tex]

[tex]b = 1 * \frac{4}{1}[/tex]

[tex]b = 4[/tex]

Substitute expression for f(x) and 4 for b in [tex]g(x) =f(bx)[/tex]

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

Calculating f(4x)

[tex]f(4x) = 2(4x) - 6[/tex]

[tex]f(4x) = 8x - 6[/tex]

Hence:

[tex]g(x) = 8x - 6[/tex]

Ver imagen MrRoyal