How do you graph this f(x)= -3/2|x|+5 if x≤4
1 answer:
Answer:
see below
Step-by-step explanation:
I enter the equation into a graphing calculator and let it do the graphing.
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If you're graphing this by hand, you start by looking for the parent function. Here, it is |x|. That has a vertex of (0, 0) and a slope of +1 to the right of the vertex and a slope of -1 to the left of the vertex.
Here, the function is multiplied by -3/2, so will open downward and have slopes of magnitude 3/2 (not 1). The graph has been translated 5 units upward, so the vertex is (0, 5).
I'd start by plotting the vertex point at (0, 5), then identifying points with slope ±3/2 either side of it. To the left, it is left 2 and down 3 to (-2, 2). The points on the right of the vertex are symmetrically located about the y-axis, so one of them will be (2, 2).
Of course, you don't plot any function values for x > 4.
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See below for the changes when the exponential function is transformed
<h3>How to determine the effect of a</h3>The exponential functions are given as:
An exponential function of the above form is represented as:
See attachment for the graph of the four functions.
<u>When a is large</u>
This is represented by
In this case, the curve of the base form is vertically stretched and it moves closer to the y-axis
<u>When a is small</u>
This is represented by
In this case, the curve of the base form is vertically stretched and it moves away from the x-axis
<u>When a is negative</u>
This is represented by
In this case, the curve of the base form is vertically stretched and is reflected across the y-axis.
Read more about function transformation at:
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