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Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-2, 0) and (0, 2)
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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 27a
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.f(x)=4x+5 a. f(6)
Guida verificata passo dopo passo1
Step 1: Understand the problem. The function f(x) = 4x + 5 is given, and you are asked to evaluate it at x = 6. This means substituting 6 for x in the function.
Step 2: Substitute x = 6 into the function. Replace every occurrence of x in f(x) = 4x + 5 with 6. The expression becomes f(6) = 4(6) + 5.
Step 3: Simplify the multiplication. Multiply 4 by 6 to get 24. The expression now becomes f(6) = 24 + 5.
Step 4: Simplify the addition. Add 24 and 5 to simplify the expression further.
Step 5: The result of f(6) is the simplified value obtained in the previous step. This is the value of the function at x = 6.
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Function Evaluation
Function evaluation involves substituting a specific value for the independent variable in a function. In this case, to evaluate f(6) for the function f(x) = 4x + 5, you replace x with 6, resulting in f(6) = 4(6) + 5. This process is fundamental in understanding how functions operate and yield outputs based on given inputs.
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Evaluating Composed Functions
Linear Functions
A linear function is a polynomial function of degree one, which can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept. The function f(x) = 4x + 5 is linear, with a slope of 4 and a y-intercept of 5. Understanding the characteristics of linear functions helps in visualizing their graphs and predicting their behavior.
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Simplification
Simplification in mathematics refers to the process of reducing an expression to its simplest form. After evaluating the function, the next step is to simplify the result, if necessary. For example, in f(6) = 24 + 5, the simplification leads to f(6) = 29, which is the final output. Mastering simplification is crucial for clear and concise mathematical communication.
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04:15Multiply Polynomials Using the Distributive Property
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