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D. The graph of g(x) is the graph of f(x) compressed vertically and then reflected over the x axis.

Step-by-step explanation:

A function shows the relationship between two or more variables.

If a function y = f(x) is reflected over the x axis, the x coordinate remain unchanged, but the y coordinate is negated. Hence the function y = f(x) becomes y = -f(x).

A function y = f(x) is compressed or stretched vertically by a factor k to give y = kf(x). If 0 < k < 1, the function is vertically compressed whereas if k > 1, the function is vertically stretched.

Given the function f(x) = x², the function is vertically compressed by a factor of 2/3 to form a function f(x)' = (2/3)x². The function is then reflected over the x axis to produce a function g(x) = (-2/3)x²

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

yes

step-by-step explanation: