Algebra 4.07: Transform Linear Functions
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.