Friday, June 7, 2019

Precalculus, Chapter 1, 1.2, Section 1.2, Problem 58

Find the intercepts of the equation y=5x and test for symmetry.

x-intercepts:


y=5xGiven equation0=5xTo find the x-intercept, we let y=00=x



The x-intercept is (0,0)

y-intercepts:


y=5xGiven equationy=50To find the y-intercept, we let x=0y=0


The y-intercept is (0,0)

Test for symmetry

x-axis:


y=5xGiven equationy=5xTo test for x-axis symmetry, replace y by y and see if the equation is still the same


The equation changes so it is not symmetric to the x-axis

y-axis:


y=5xGiven equationy=5xTo test for y-axis symmetry, replacex by x and see if the equation is still the samey=5x


The equation changes so it is not symmetric to the y-axis

Origin:


y=5xGiven equationy=5xTo test for origin symmetry, replace both x by x and y by y and see if the equation is still the samey=5xy=5x


The equation is still the same so it is symmetric to the origin.

Therefore, the equation y=5x has an intercepts (0,0) and it is symmetric to the origin.

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