If f(x) is an even function and (6, 8) is one the points on the graph of f(x), which reason explains why (-6, 8) must also be a point
on the graph?
since the function is even the outputs of a negative x-value and a positive x-value are the same.
since the function is even the outputs of a negative y-value and a positive y-value are the same.
the graph has rotational symmetry, so the point will be reflected across the y-axis.
the graph has rotational symmetry, so the point will be rotated 90 degrees about the origin.

Atest of sobriety involves measuring the subject's motor skills. a sample of 31 randomly selected sober subjects take the test and produce a mean score of 64.4 with a standard deviation of 2. a claim is made that the true mean score for all sober subjects is equal to 65. for each part below, enter only a numeric value in the answer box. for example, do not type "z =" or "t =" before your answers. round each of your answers to 3 places after the decimal point. (a) calculate the value of the test statistic used in this test. test statistic's value = (b) use your calculator to find the p-value of this test. p-value = (c) use your calculator to find the critical value(s) used to test this claim at the 0.2 significance level. if there are two critical values, then list them both with a comma between them. critical value(s) =