Page 411 - Algebra 1

INVE6STIGATION
Transforming Linear Functions
A family of functions share common characteristics. A parent function is the simplest function in a family of functions. The parent function for a linear function is f(x) = x. Functions in the family are transformations of the parent function. The graph of f(x) = x is shown below.
y
8
4
O
x
-8
-4
-4
4
8
-8
Hint
Function notation, f(x), can be used in place of y.
Math Reasoning
Write Why do all linear functions belong to the same family of functions?
O
y
4
2
x
-4
-2
2
-2
f
x
4
=x-
4
y
2
f(x) = x
x
O
-4
-2
2
4
Online Connection www.SaxonMathResources.com
A translation shifts every point in a figure the same distance in the same direction. A translation can be thought of as a slide. A translation of a linear function is also referred to as a vertical change.
f(x) = x
()4
1. Graph f(x) = x, f(x) = x + 3, and f(x) = x - 2 on the same coordinate grid.
2. Generalize Compare the graphs of f(x) = x + 3 and f(x) = x - 2 to the parent function. Use the y-intercept in your comparison.
A vertical stretch or compression changes the rate of change of a linear equation.
f(x) = 5x
3. Graph f(x) = x, f(x) = 3x, and f(x) = _1 x on the same coordinate grid. 3
4. Generalize Discuss how the slope of a line is related to the steepness of a line.
396 Saxon Algebra 1