Transformations of Functions

Describe the transformations of f(x) when compared to the parent function.
f(x)=(x+7)²

• horizontal shift left 7 units

• horizontal shift right 7 units

• vertical shift up 7 units

• vertical shift down 7 units

In the equation f(x)=5(x+3)²-10 what effect does the 5 do when compared to the parent function?

• Vertical stretch by a factor of 5

• Vertical shrink/compress by a factor of 5

• Reflect over x-axis

• Vertical shift up 5 units

If the blue is f(x)=x^2, the red must be

• g(x)=(x+3)²

• g(x)=(x-3)²

• g(x)=x²+3

• g(x)=x²-2

Quadratic functions q and w are graphed on the same coordinate grid.  The vertex of the graph of q is 18 units below the vertex of the graph of w.  Which pair of functions could have been used to create the graphs of q and w?

• q(x) = 18x² and w(x) = x²

• q(x) = x² + 18 and w(x) = x²

• q(x) = -18x² and w(x) = x²

• q(x) = x² - 18 and w(x) = x²

Linear function f\left(x\right)=x is graphed on a coordinate plane. The graph of a new line is formed by changing the slope of the original line to \frac{2}{3} and the y-intercept to 4 . Which statement about the relationship between these two graphs is true?

• The graph of the new line is steeper than the graph of the original line, and the y-intercept has been translated down.

• The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up.

• The graph of the new line is steeper than the graph of the original line, and the y-intercept has been translated up.

• The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated down.

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The graph of f\left(x\right)=x^2 was transformed to create the graph of g\left(x\right)=f\left(x\right)-9. Which statement about the graphs is true?