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2.2: Linear Functions

https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/02%3A_Linear_Functions/2.02%3A_Linear_Functions

The ordered pairs given by a linear function represent points on a line. Linear functions can be represented in words, function notation, tabular form, and graphical form. The rate of change of a line...The ordered pairs given by a linear function represent points on a line. Linear functions can be represented in words, function notation, tabular form, and graphical form. The rate of change of a linear function is also known as the slope. An equation in the slope-intercept form of a line includes the slope and the initial value of the function. The initial value, or y-intercept, is the output value when the input of a linear function is zero.

6.1: Linear Equations - Applications

https://math.libretexts.org/Courses/Highline_College/Math_081_091%3A_CAM_Aligned_Textbook/06%3A_Linear_Equations_and_Functions/6.01%3A_Linear_Equations_-_Applications

The ordered pairs given by a linear function represent points on a line. Linear functions can be represented in words, function notation, tabular form, and graphical form. The rate of change of a line...The ordered pairs given by a linear function represent points on a line. Linear functions can be represented in words, function notation, tabular form, and graphical form. The rate of change of a linear function is also known as the slope. An equation in the slope-intercept form of a line includes the slope and the initial value of the function. The initial value, or y-intercept, is the output value when the input of a linear function is zero.

1.2: Basic Classes of Functions

https://math.libretexts.org/Courses/College_of_Southern_Nevada/Calculus_(Hutchinson)/01%3A_Functions_and_Graphs_(Precalculus_Review)/1.02%3A_Basic_Classes_of_Functions

Figure

$\PageIndex{9}$ : (a) For

$c>0$ , the graph of

$y=f(x)+c$ is a vertical shift up

$c$ units of the graph of

$y=f(x)$ . (b) For

$c>0$ , the graph of

$y=f(x)−c$ is a vertical shift down ...Figure

$\PageIndex{9}$ : (a) For

$c>0$ , the graph of

$y=f(x)+c$ is a vertical shift up

$c$ units of the graph of

$y=f(x)$ . (b) For

$c>0$ , the graph of

$y=f(x)−c$ is a vertical shift down c units of the graph of

$y=f(x)$ . For

$c>0$ , the graph of

$f(x+c)$ is a shift of the graph of

$f(x)$ to the left

$c$ units; the graph of

$f(x−c)$ is a shift of the graph of

$f(x)$ to the right

$c$ units.

1.3: Basic Classes of Functions

https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/01%3A_Functions_and_Graphs/1.03%3A_Basic_Classes_of_Functions

We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define gene...We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter. We finish the section with piecewise-defined functions and take a look at how to sketch the graph of a function that has been shifted, stretched, or reflected from its initial form.

2.1: Linear Functions

https://math.libretexts.org/Courses/Hartnell_College/MATH_25%3A_PreCalculus_(Abramson_OpenStax)/02%3A_Linear_Functions/2.01%3A_Linear_Functions

The ordered pairs given by a linear function represent points on a line. Linear functions can be represented in words, function notation, tabular form, and graphical form. The rate of change of a line...The ordered pairs given by a linear function represent points on a line. Linear functions can be represented in words, function notation, tabular form, and graphical form. The rate of change of a linear function is also known as the slope. An equation in the slope-intercept form of a line includes the slope and the initial value of the function. The initial value, or y-intercept, is the output value when the input of a linear function is zero.

1.2: Basic Classes of Functions

https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_1_(Sklar)/01%3A_Functions_and_Graphs/1.02%3A_Basic_Classes_of_Functions

We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define gene...We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter. We finish the section with piecewise-defined functions and take a look at how to sketch the graph of a function that has been shifted, stretched, or reflected from its initial form.

1.3: Basic Classes of Functions

https://math.libretexts.org/Courses/Laney_College/Math_3A%3A_Calculus_1_(Fall_2022)/01%3A_Functions_and_Graphs/1.03%3A_Basic_Classes_of_Functions

We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define gene...We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter. We finish the section with piecewise-defined functions and take a look at how to sketch the graph of a function that has been shifted, stretched, or reflected from its initial form.

1.2: Basic Classes of Functions

https://math.libretexts.org/Courses/Reedley_College/Calculus_I_(Casteel)/01%3A_Functions_and_Graphs/1.02%3A_Basic_Classes_of_Functions

We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define gene...We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter. We finish the section with piecewise-defined functions and take a look at how to sketch the graph of a function that has been shifted, stretched, or reflected from its initial form.

1.2: Basic Classes of Functions

https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_hdagnew@ucdavis.edu/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2%2F%2F1%3A_Functions_and_Graphs_(Review)/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2%2F%2F1%3A_Functions_and_Graphs_(Review)%2F%2F1.2%3A_Basic_Classes_of_Functions

For

$c>0$ , the graph of

$f(x+c)$ is a shift of the graph of

$f(x)$ to the left

$c$ units; the graph of

$f(x−c)$ is a shift of the graph of

$f(x)$ to the right

$c$ units. For example, the...For

$c>0$ , the graph of

$f(x+c)$ is a shift of the graph of

$f(x)$ to the left

$c$ units; the graph of

$f(x−c)$ is a shift of the graph of

$f(x)$ to the right

$c$ units. For example, the graph of the function

$f(x)=3x^2$ is the graph of

$y=x^2$ stretched vertically by a factor of 3, whereas the graph of

$f(x)=x^2/3$ is the graph of

$y=x^2$ compressed vertically by a factor of

$3$ (Figure

$\PageIndex{8}$ ).

7.4: Point-Slope Form of a Line

https://math.libretexts.org/Courses/Honolulu_Community_College/Math_75X%3A_Introduction_to_Mathematical_Reasoning_(Kearns)/07%3A_Introduction_to_Graphing/7.04%3A_Point-Slope_Form_of_a_Line

In the previous section we learned that if we are provided with the slope of a line and its

$y$ -intercept, then the equation of the line is

$y = mx + b$ , where

$m$ is the slope of the line and \...In the previous section we learned that if we are provided with the slope of a line and its

$y$ -intercept, then the equation of the line is

$y = mx + b$ , where

$m$ is the slope of the line and

$b$ is the

$y$ -coordinate of the line’s

$y$ -intercept. If we use the point

$P(−1,2)$ for

$(x_0,y_0)$ , we get the answer on the left, but if we use the point

$Q(3,−4)$ for

$(x_0,y_0)$ , we get the answer on the right.

2.2: Linear Functions

https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_2e_(OpenStax)/02%3A_Linear_Functions/2.02%3A_Linear_Functions

The ordered pairs given by a linear function represent points on a line. Linear functions can be represented in words, function notation, tabular form, and graphical form. The rate of change of a line...The ordered pairs given by a linear function represent points on a line. Linear functions can be represented in words, function notation, tabular form, and graphical form. The rate of change of a linear function is also known as the slope. An equation in the slope-intercept form of a line includes the slope and the initial value of the function. The initial value, or y-intercept, is the output value when the input of a linear function is zero.

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