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
#LearnwithBrainly
