Question

Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(-10x)?
A.
It is the graph of f(x) reflected about the x-axis and shrunk vertically by a factor of 10.
B.
It is the graph of f(x) reflected about the y-axis and stretched horizontally by a factor of 10.
C.
It is the graph of f(x) reflected about the x-axis and shrunk horizontally by a factor of 10.
D.
It is the graph of f(x) reflected about the x-axis and stretched horizontally by a factor of 10.

Answer 1

The statement which describes correctly the graph of g(x) is " It is the graph of f(x) reflected about the x-axis and shrunk horizontally by a factor of 10 " ⇒ answer C

Step-by-step explanation:

Let us revise some transformation

A vertical stretching is the stretching of the graph away from the x-axis

A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis.

• If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by k.
• If 0 < k < 1 (a fraction), the graph of y = k•f(x) is the graph of f(x) vertically shrunk (or compressed) by multiplying each of its y-coordinates by k
• f k should be negative, the vertical stretch or shrink is followed by a reflection across the x-axis.  

A horizontal stretching is the stretching of the graph away from the y-axis

A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis.

• If k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k.
• If 0 < k < 1 (a fraction), the graph of y = f(k•x) is the graph of f(x) horizontally stretched by dividing each of its x-coordinates by k
• If k should be negative, the horizontal stretch or shrink is followed by a reflection across the y-axis.

∵ f(x) = x

∵ g(x) = f(-10x)

- Substitute x by -10x

∴ g(x) = -10x

∵ x is changed to 10x

- x multiplied by a number means shrink or stretch horizontally

∵ k = 10

∵ 10 > 1

∴ The graph of f(x) is shrunk horizontally by a factor of 10

∵ The value of g(x) is negative

- The negative sign of g(x) means reflection across x-axis

∴ The graph of f(x) is reflected about the x-axis

The statement which describes correctly the graph of g(x) is " It is the graph of f(x) reflected about the x-axis and shrunk horizontally by a factor of 10 "

Learn more:

You can learn more about reflection in brainly.com/question/5017530

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