Algebra 4.07: Transform Linear Functions

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Think about the graphs of the equations y = 2x and y = 2x + 7. What effect does adding 7 in the second equation have on the graph of the first equation?

The graph is translated up 7 units.

Which transformation takes f(x)=2x+4 to g(x)=4x+4 ?

a horizontal compression by a factor of 12

Answer the following question about the functions f(x)=9x+2 and g(x)=3x+2 . What transformation takes the graph of function f to the graph of function g?

a horizontal stretch by a factor of 3

What transformation takes f(x)=9x+3 to g(x)=3x+3 ?

a horizontal stretch by a factor of 3

transformations

a one-to-one mapping between two sets of points

What transformation takes f(x)=4x−7 to g(x)=−4x−7 ?

a reflection across the y-axis

Which transformation takes f(x)=3x−2 to g(x)=−3x+2 ?

a reflection over the x-axis

Which transformations take f(x)=3x+1 to g(x)=−3x−5 ?

a reflection over the x-axis and a translation 4 units down

reflections

a transformation that flips a graph across a line, creating a mirror image

stretches

a transformation that pulls a graph away from an axis

compressions

a transformation that pushes a graph toward an axis

translations

a transformation that slides a figure in a straight path without rotation or reflection

f(x)=2x and g(x)=2(x−4) . What transformation occurs from function f to function g?

a translation 4 units right

Answer the following question about the functions f(x)=x+2 and g(x)=−5x−10 . Which transformations take the graph of function f to the graph of function g? Select each correct answer.

a vertical stretch by a factor of 5 a reflection over the x-axis

Answer the following questions about the functions f(x)=3x and g(x)=f(x−2) . What equation shows the correct rule for function g? What statement describes the transformation between function f and function g.

g(x)=3x−6 translation right 2 units

Answer the following questions about the functions f(x)=8x+2 and h(x)=1/2 ⋅ f(x) . Write the equation for function h. Enter your response in the box. What statement describes the transformation between function f and function h.

h(x)=1/2 ⋅ f(x) h(x)=1/2(8x+2) h(x)=4x+1 vertical compression by a factor of 1/2

indicate whether the equation is in standard form. −x+3y=15 4y−4x=16 13+5y=6x x+y=1

−x+3y=15 is in standard form. 4y−4x=16 is not in standard form because the variable terms are in the wrong order. 13+5y=6x is not in standard form because the two variable terms are not both on the left side. x+y=1 is in standard form. A, B, and C are all 1.


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