Linear Equations Transformations

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

What is the y-intercept of
2x-5y=35?

• (0,-7)

• (-7,0)

• (35/2, 0)

• (0,35/2)

The parent function f(x)=x is transformed to create the function g(x)=f(x)-1. Which graphs best represents the transformation of f(x)?

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Determine the effects on the graph of the parent function ​f(x)=x for the ​g(x)=f(x)−5 function.

• The graph shifts 5 units to the left.

• The graph shifts 5 units down.

• The graph shifts 5 units to the right.

• The graph shifts 5 units up

Find an equation for​ g(x) when ​g(x)=−​f(x).

​f(x)=8x

​g(x)= ____

• -8x

• -8

• 8x

• 8

Determine the effects on the graph of the parent function ​f(x)=x for the ​g(x)=f(x−6) function.

• The graph shifts right 6 units.

• The graph shifts left 6 units.

Which transformation on f(x) = x is g(x) = -f(x)

• Reflection across the y-axis

• The slope will be less steep

• The graph will be wider

• Reflection across the x-axis.

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• Graph g shifted down 3 units

• Graph g shifted down 4 units

• Graph g shifted up 4 units

• Graph g reflected

Which of the following g(x) equations is vertically stretched and shifted down from f(x) = x?

• g(x) = 2 f(x) + 6

• g(x) = 1/2 f(x) + 6

• g(x) = 2 f(x) - 6

• g(x) = 1/2 f(x) - 6

f\left(x\right)=x and g\left(x\right)=2x-4
Which statement about the relationship of these two graphs is true?

• The graph of g is steeper than the graph of f, and the y-intercept has been translated up.

• The graph of g is less steep than the graph of f, and the y-intercept has been translated up.

• The graph of g is less steep than the graph of f, and the y-intercept has been translated down.

• The graph of g is steeper than the graph of f, and the y-intercept has been translated down.