Linear Transformations to Parent Function

The graph of f(x) = x is transformed to create the graph of g(x) = 1/2 f(x) + 3. Complete the statement to compare the graphs of f and g.

The graph of g is​ (a)   than the graph of f and has a y-intercept that is ​ (b)   that of f.

• steeper
• less than
• less steep
• greater than

The graph of the function f(x) = x is transformed to form function g(x) such that g(x) = 3f(x). Which graph represents f and g?

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The graph of linear function h is shown on the grid.

Given f(x) = x and h(x) = af(x), what is the value of a?

Mathematical Equivalence

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Linear parent function f is graphed on the grid.

Which graph best represents h(x) = -f(x) + 3?

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The graphs of linear functions f and g are shown on the grid.

Which function is best represented by the graph of g?

A student graphed f(x) = x and g(x) = f(x) + 3 on the same coordinate grid.

Which statement describes how the graphs of f and g are related?

• The graph of f is shifted 3 units up to create the graph of g.

• The graph of f is steeper than the graph of g.

• The graph of f is shifted 3 units down to create the graph of g.

• The graph of f is less steep than the graph of g.

Linear function f(x) = x is graphed on a coordinate plane. The graph of a new line is formed by changing the slope of the original line to 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.

The linear parent function, f(x) = x, is transformed to g(x) = f(x + 3). Describe the transformation.

• g(x) is shifted up 3 units

• g(x) is shifted down 3 units

• g(x) is shifted left 3 units

• g(x) is shifted right 3 units

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation.

• g(x) is shifted up 6 units

• g(x) is shifted down 6 units

• g(x) is shifted left 6 units

• g(x) is shifted right 6 units

This is the parent function f(x). If the line, g(x), is less steep, what could the equation of g(x) be?

• 4f(x)

• 1/4f(x)

• -4f(x)

• f(x) - 4

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AI.9.3.E