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Chapter 11: Problem 234

Graph the constant function \(2 \mathrm{y}=4\).

Short Answer

Expert verified
The graph of the constant function \(2y = 4\) is a horizontal line at \(y = 2\), running parallel to the x-axis.

Step by step solution

01

Rewrite the equation in the form \(y = f(x)\)

First, we need to rewrite the equation \(2y = 4\) in the form \(y = f(x)\). To do this, simply solve for \(y\): \[ y = \frac{4}{2} \]
02

Determine the type of function and its key features

Now that we have the equation in the form \(y = f(x)\), it's much easier to see the type of function and its key features. In this case, the equation is \(y = \frac{4}{2}\), which simplifies to \(y = 2\). Since there is no \(x\) variable in the equation, this is a horizontal line at \(y = 2\).
03

Plot the function on a coordinate plane

To plot the function, we can start by drawing a coordinate plane with an x-axis and a y-axis. Our function is a horizontal line at \(y = 2\), so we'll draw a straight line through the point \((0, 2)\) that is parallel to the x-axis. This line represents the graph of the constant function \(2y = 4\). That's it! The graph of the constant function \(2y = 4\) is a horizontal line at \(y = 2\), running parallel to the x-axis.

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Most popular questions from this chapter

Write the equation in slope-intercept form; specify the slope and the \(y\) -intercept of the line. Sketch the graph of the equation. \(2 \mathrm{x}-3 \mathrm{y}=5\)

Graph the function \(3 \mathrm{x}-5\).

The slope and one point of a line are given. Is the Y-intercept positive or negative? (a) \(\mathrm{m}=22 / 7,(1, \pi)\) b) \(\mathrm{m}=\sqrt{2},(1,1.414)\)

If \(\mathrm{f}(\mathrm{x})=-2 \mathrm{x}-5\), find the (a) slope, (b) \(\mathrm{x}\) -intercept, and (c) \(\mathrm{y}\) -intercept, (d) Graph the function

Sketch the graph of the function \(\mathrm{H}=\\{[\mathrm{x}, \mathrm{H}(\mathrm{x})] \mid \mathrm{H}(\mathrm{x})=6\\}\).
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