Families of Linear Functions Graph f(x)=x+b for b=(1)/(2), b=1, and b=2, all on the same set of

Name: Problem 38, Chapter 2: Algebra and Trigonometry
Uploaded: 2019-06-27T05:05:17-08:00
Duration: 2 min 34 s
Channel: Ernest Castorena
Description: Families of Linear Functions Graph f(x)=x+b for b=(1)/(2), b=1, and b=2, all on the same set of axes. How does increasing the value of b affect the graph of f ? What about the rate of change of f ?

step 1 graph several functions on a shared xes. So they want us to graph f of x is equal to x plus b. F

Question

Families of Linear Functions Graph $f(x)=x+b$ for $b=\frac{1}{2}, b=1,$ and $b=2,$ all on the same set of axes. How does increasing the value of $b$ affect the graph of $f ?$ What about the rate of change of $f ?$

   Families of Linear Functions Graph $f(x)=x+b$ for
$b=\frac{1}{2}, b=1,$ and $b=2,$ all on the same set of axes. How
does increasing the value of $b$ affect the graph of $f ?$ What
about the rate of change of $f ?$

Algebra and Trigonometry

James Stewart,… 4th Edition

Chapter 2, Problem 38

Instant Answer

Solved by Expert Ernest Castorena

06/27/2019

Step 1

Step 1: First, we need to graph the function $f(x)=x+b$ for $b=\frac{1}{2}, b=1,$ and $b=2$. Show more…

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Families of Linear Functions Graph $f(x)=x+b$ for $b=\frac{1}{2}, b=1,$ and $b=2,$ all on the same set of axes. How does increasing the value of $b$ affect the graph of $f ?$ What about the rate of change of $f ?$

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Key Concepts

Linear Functions

Linear functions are functions of the form f(x) = mx + b, where m represents the slope and b represents the y-intercept. They produce straight-line graphs and are fundamental in understanding relationships with a constant rate of change.

Slope (Rate of Change)

The slope of a linear function indicates how much the function's value changes for a unit change in x. It represents the rate of change, and for linear functions, this rate remains constant no matter the value of the y-intercept.

Vertical Shift (y-intercept)

The y-intercept, denoted by b in the function f(x) = x + b, determines the point at which the graph intersects the y-axis. Changing the value of b results in a vertical translation of the graph without altering its slope or rate of change.

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