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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.
4.4: Logarithmic Functions
https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/04%3A_Exponential_and_Logarithmic_Functions/4.04%3A_Logarithmic_Functions
The inverse of an exponential function is a logarithmic function, and the inverse of a logarithmic function is an exponential function.
4.6: Exponential and Logarithmic Functions
https://math.libretexts.org/Bookshelves/Calculus/Calculus_(Guichard)/04%3A_Transcendental_Functions/4.06%3A_Exponential_and_Logarithmic_Functions
An exponential function has the form $a^x$ , where $a$ is a constant. The logarithmic functions are the inverses of the exponential functions, that is, functions that "undo'' the exponential funct...An exponential function has the form $a^x$ , where $a$ is a constant. The logarithmic functions are the inverses of the exponential functions, that is, functions that "undo'' the exponential functions.
7.4: Properties of the Logarithm
https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/07%3A_Exponential_and_Logarithmic_Functions/7.04%3A_Properties_of_the_Logarithm
We can use the properties of the logarithm to expand logarithmic expressions using sums, differences, and coefficients. A logarithmic expression is completely expanded when the properties of the logar...We can use the properties of the logarithm to expand logarithmic expressions using sums, differences, and coefficients. A logarithmic expression is completely expanded when the properties of the logarithm can no further be applied.
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.
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 $\PageIndex{8}$ ).
4.3: Logarithmic Functions
https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/04%3A_Exponential_and_Logarithmic_Functions/4.03%3A_Logarithmic_Functions
The inverse of an exponential function is a logarithmic function, and the inverse of a logarithmic function is an exponential function.
4.4: Logarithmic Functions
https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Professor_Holz'_Topics_in_Contemporary_Mathematics/04%3A_Population_Growth_Models/4.04%3A_Logarithmic_Functions
The inverse of an exponential function is a logarithmic function, and the inverse of a logarithmic function is an exponential function.

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