Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 41

Chapter 3, Problem 41

In Exercises 39–48, give the slope and y-intercept of each line whose equation is given. Then graph the linear function. f(x) = -2x+1

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Identify the given linear function: $f(x) = -2x + 1$.

Recall that a linear function in slope-intercept form is written as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Compare the given function $f(x) = -2x + 1$ to the slope-intercept form to find the slope $m = -2$ and the y-intercept $b = 1$.

To graph the function, start by plotting the y-intercept point at $(0, 1)$ on the coordinate plane.

From the y-intercept, use the slope $-2$ (which means a rise of $-2$ and a run of $1$) to find another point by moving down 2 units and right 1 unit, then draw the line through these points.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Slope of a Linear Function

The slope represents the rate of change of the function and indicates how steep the line is. It is the coefficient of x in the equation f(x) = mx + b, where m is the slope. A negative slope means the line decreases as x increases.

Y-Intercept of a Linear Function

The y-intercept is the point where the line crosses the y-axis, given by the constant term b in the equation f(x) = mx + b. It represents the value of the function when x is zero, providing a starting point for graphing the line.

Graphing a Linear Function

Graphing involves plotting the y-intercept on the coordinate plane and using the slope to find another point by moving vertically and horizontally. Connecting these points with a straight line visually represents the function.

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Textbook Question

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) = -2x, g(x) = -2x-1

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