Algebra Transformation

The linear parent function, f(x) = x, is transformed to g(x) = f(x + 6). Does this result in a horizontal or vertical translation?

• horizontal

• vertical

Which transformation will occur if f(x) = x is replaced with 2f(x)?

• Vertical stretch by a factor of 2

• Vertical compression by a factor of 1/2

• Vertical translation up by 2 units.

• Horizontal compression by a factor of 1/2

If the graph of the parent function f(x) = x is shifted 7 units up and is horizontally compressed by a factor of 3, what is the function?

• g(x) = f(7x) + 3

• g(x) = 3f(x) - 7

• g(x) = f(3x) + 7

• g(x) = 7x - 3

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

• Graph g rotated

• Graph g translated down 4 units

• Graph g translated up 4 units

• Graph g reflected

How did the equation f(x) = x change if

g(x) = 1/2f(x) + 11

• Vertical stretch and shift up 11

• Horizontal shrink and shift down 11

• Vertical shrink and shift up 11

• Horizontal stretch and shift down 11

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?

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.

Let g(x) be the indicated transformation of f(x). Write the rule for g(x). f(x)= 12x + 18, vertical stretch by a factor of 3

• g(x)= 36x + 54

• g(x)= 4x + 6

• g(x)= 36x + 18

• g(x)= 4x + 18

The linear function f(x) = x - 3, is transformed to h(x) = 2(x - 3). How has the graph changed.

• The slope changes by a factor of 2 and the y-intercept does not change.

• Both the slope and y-intercept change by a factor of 2.

• The slope does not change. The y-intercept changes by a factor of 2.

• The slope and y-intercept DO NOT change.

The linear equation f(x) = 5x, is transformed to k(x) = 5x - 6. How has the graph of the function changed.

• The slope and y-intercept DO NOT change.

• The slope changes by a factor of -6 and the y-intercept does not change.

• The slope and y-intercept change by a factor of -6.

• The slope does not change. The y-intercept changes by a decrease of 6.