Use point-by-point plotting to sketch the graph of the equation.
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Question

Quizplus · Accepted Answer

The equation appears to be a sinusoidal function. Using point-by-point plotting, we can determine the amplitude, period, and phase shift of the function.

We will first find the midline, or horizontal axis, of the function. This is the average of the maximum and minimum values of the function. From the equation, we can see that the maximum value is 3 and the minimum value is -1. Therefore, the midline is:
midline = (3 + (-1))/2 = 1

Next, we will find the amplitude of the function, which is half the distance between the maximum and minimum values. Therefore, the amplitude is: 
amplitude = (3 - (-1))/2 = 2

Now, we need to find the period. The period is the distance between two consecutive peaks or two consecutive troughs of the function. The general formula for the period is:
period = 2π/|B|

From the equation, we can see that B = 1/2. Therefore, the period is:
period = 2π/|1/2| = 4π

Finally, we need to find the phase shift of the function. The phase shift is the horizontal shift of the function compared to its standard position. The general formula for the phase shift is:
phase shift = -C/B

From the equation, we can see that C = 1. Therefore, the phase shift is:
phase shift = -1/(1/2) = -2

Using these values, we can sketch the graph of the function. The graph should have a midline of y = 1, an amplitude of 2, a period of 4π, and a phase shift of -2.

By testing each of the options, we can see that choice B matches this description. The equation can be simplified to $y=x+1$. 
We can plot two points to sketch the graph:
When $x=0$, $y=1$. So plot the point $(0,1)$.
When $x=1$, $y=2$. So plot the point $(1,2)$.
Then connect the points with a straight line to obtain the graph of the equation $y=x+1$. 
Only option B matches this graph.

Use Point-By-Point Plotting to Sketch the Graph of the Equation