Question

The graph of a function never has two different points with the same x-coordinate because .
A. each input value is mapped to more than one output value.
B. each input value is mapped to a single output value.
C. the graph of a function is a vertical line.
D. the graph of a function cannot be a straight line

Answer 1

a function is a relationship where each unique value of the input value is mapped to a single output value. if you know the input value, and the definition of the function, you can determine the output value, and the same input value will always produce the same output value.

Answer 2

so its b?

Answer 3

i got it

Answer 4

well, let's go through the choices.

D - cannot be a straight line - just about every straight line IS a function, except for a vertical line, which would have every possible value associated with the same input value. wouldn't know which one to pick.

C also gets ruled out, see D

A - every input value has multiple output values - again, that fails the test of a single predictable output value for each input value

B on the other hand is perfect! 😀

Answer 5

i posted another question can i get help with it
What is the y-intercept of the function, represented by the table of values below?
http://media.apexlearning.com/Images/201307/25/8aa86f30-2d4f-48a0-b665-daed84aab166.jpg
A. 8
B. 6
C. 2
D. 4

Answer 6

if you move one unit to the right on the x-axis, how much does the y-value change?

Answer 7

what do you mean?

Answer 8

@DyingSenpai what I mean is this:

you have a table of data:

\[
\begin{array}{cc}
x&y\\
\hline
-2 & 16 \\
1 & 4 \\
2 & 0 \\
4 & -8 \\
7 & -20 \\
\end{array}
\]

If you go from \(x=0\) to \(x=1\) (1 unit to the right on the x-axis), how does the value of \(y\) change?

This change is the slope of the line, and from it and another point in the table, you can find what the value of the y-intercept will be, which is simply the value of \(y\) when \(x=0\).

From \(x=1\) to \(x=2\), \(y\) goes from \(4\) to \(0\). If we go 2 more units to the right (positive direction on the x-axis), \(y\) goes from \(0\) to \(-8\). Clearly, for each unit we go to the right, \(y\) decreases by \(4\). The flip side of that is that for each unit we go to the left (negative direction on the x-axis\), \(y\) increases by \(4\). We know that at \(x=1,\, y=4\), and at \(x=-2,\ y=16\). What will the value of \(y\) be at \(x = 0\)?