Please help me very quickly! Please help.

Question

Question 1: Use a table to compress the function y = f(x) vertically by a factor of 1/2. Identify the graph of the function and its transformation.

A.)

B.)

C.)

D.)

Question 2: Identify the relation that is a function.

A.) days of the week to the months of the year

B.) city name to state name

C.) last name to phone number

D.) number of apples purchased to the cost of the apples

Question 3: Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.

A.) function

B.) not a function; (1, 3) and (3, 0)

C.) not a function; (1, 3) and (5, −3)

D.) not a function; (0, 0) and (3, 0)

Please give solution and explanation please.

Answer 1

Hi, Jenna.

For Question 1, compressing a graph vertically by a factor of 1/2 means that each y-coordinate on the graph is multiplied by 1/2. For instance, the given graph appears to cross the y-axis at the point (0, 1). The transformed graph would therefore cross the y-axis at the point (0, 1/2).

Note that any point on the graph with a y-coordinate of 0 (that is, a point where the graph intersects the x-axis) does not change because multiplying 0 by 1/2 is still 0.

The only answer choice that shows a solid graph passing through (0, 1/2) is choice B. Notice that this graph has the same x-intercepts as the given (dashed) graph, which confirms that this is the correct choice.

To answer Question 2, you have to remember that a relation is a function only when each input is paired with a unique output. Choice A appears to be pairing a day like Monday to a month like September. But Monday can also be paired with every other month, so the output "September" is not unique. Likewise, for choice B, a city name like Springfield can be paired with a state like Illinois. But there are many other states with a city called "Springfield" (which is why you can never know which state the Simpsons live in!). For choice B, a person's last name can be paired with more than one phone number if that person has more than one phone (such as a landline and a cell phone). Only choice D appears to a be function if you assume that all apples cost the same. Whatever number of apples you buy uniquely determines the cost of the apples.

For Question 3, you need to know the vertical line test, which says that a graph represents a function if and only if no vertical line passes through more than one point on the graph. For the graph shown, the vertical line test holds, so A is the correct choice. (Note that if you rotate the graph 90 degrees (either clockwise or counterclockwise) about the origin, you'd get a graph that does not represent a function because you'd be able to draw vertical lines through 2 or more points on the graph.)

Doug