Domanda del libro di testo
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3| b. f(-5)
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 3, Problema 39
Graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = x, g(x) = x + 3
Guida verificata passo dopo passo1
Identify the given functions: \(f(x) = x\) and \(g(x) = x + 3\).
Create a table of values for \(x\) starting from \(-2\) to \(2\). For each \(x\), calculate \(f(x)\) and \(g(x)\) separately.
For \(f(x) = x\), the values will be the same as \(x\) itself. For \(g(x) = x + 3\), add 3 to each \(x\) value to find the corresponding \(g(x)\) values.
Plot the points for both functions on the same coordinate system using the calculated values. For example, plot \((x, f(x))\) and \((x, g(x))\) for each \(x\) from \(-2\) to \(2\).
Observe the graphs: describe how the graph of \(g\) is related to the graph of \(f\). Consider how adding 3 to \(x\) affects the position of the graph compared to \(f(x)\).
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Function Notation and Evaluation
Function notation, such as f(x) and g(x), represents a rule that assigns each input x to exactly one output. Evaluating a function means substituting a specific value for x to find the corresponding output, which is essential for plotting points on a graph.
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Evaluating Composed Functions
Graphing Linear Functions
Linear functions like f(x) = x produce straight-line graphs. Plotting points for selected x-values and connecting them helps visualize the function. Understanding the slope and intercept aids in sketching and comparing graphs.
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5:26Graphs of Logarithmic Functions
Vertical Translation of Graphs
Adding a constant to a function, as in g(x) = x + 3, shifts the graph vertically. Specifically, g(x) is the graph of f(x) moved up by 3 units. Recognizing this transformation helps describe the relationship between the two graphs.
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3:12Determining Vertical Asymptotes
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