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How do you graph #y = | -3x+5 |#?

Answer 1

Julia Adams

See below.

We need to graph to lines.

#y=-3x+5# and #y=3x-5#

We need to find the x axis intercept of these. Which is:

#5/3#

Since we can only have positive y values, we need to graph these piecewise.

For #color(white)(88)x>=5/3->3x-5#

For #color(white)(88)x<=5/3->-3x+5#

Graph:

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Answer 2

Eva Abramson

To graph the equation (y = | -3x + 5 |):

Set up a table of values by choosing several x-values and finding the corresponding y-values:

x -2 -1 0 1 2
y 11 8 5 2 1
Plot the points from the table on the coordinate plane.
Because of the absolute value function, the graph will reflect any points below the x-axis to their corresponding points above the x-axis.
Draw a smooth curve connecting the points, making sure to maintain the symmetry of the graph due to the absolute value function.
Label the graph as (y = | -3x + 5 |).

x	-2	-1	0	1	2
y	11	8	5	2	1

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.