Question

Graph each equation . Let $x=-3,-2,-1,0$ $1,2,$ and 3. $$y=|x|+1$$

   Graph each equation . Let $x=-3,-2,-1,0$ $1,2,$ and 3.
$$y=|x|+1$$

Precalculus

Robert Blitzer 6th Edition

Chapter 1, Problem 23

Instant Answer

Solved by Expert Erika Bustos

08/20/2021

Step 1

We will substitute the values $x=-3,-2,-1,0,1,2,3$ into the equation and solve for $y$. Show more…

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Graph each equation . Let $x=-3,-2,-1,0$ $1,2,$ and 3. $$y=|x|+1$$

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Key Concepts

Graphing by Plotting Points

Graphing a function by plotting specific x-values and calculating corresponding y-values is a fundamental technique in algebra and precalculus. This method helps visualize the behavior and shape of the function by mapping individual points onto the coordinate plane.

Absolute Value Function

The absolute value function takes any real number and outputs its non-negative value. It is defined piecewise, meaning it outputs x when x is non-negative and -x when x is negative. This concept is crucial for understanding how the function behaves over its entire domain.

Function Transformation (Vertical Shift)

The equation y = |x| + 1 represents a vertical shift of the standard absolute value function upward by one unit. Understanding how adding or subtracting a constant affects the graph of a function is key in studying function transformations.

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