graph the relation in the table. then use the vertical-line test. is the relation a function? -1 & 3, 1 & -1, 2 & 2,
1 & 3
1 answer:
Answer:
this relation is not a function.
Step-by-step explanation:
Given relation is
(-1, 3) (1,-1) (2,2) and (1,3)
Now plot all the ordered pairs on the graph
Then we draw vertical lines through these points
If any vertical line crosses two points then this relation is not a function
The graph is attached below
We can see that the red vertical line crosses both points (1,-1) and (1,3)
It does not passes vertical line test.So this relation is not a function.
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The quadratic function given by:
is in vertex form. The graph of is a parabola whose axis is the vertical line
and whose vertex is the point
. So:
To translate the graph of a function to the right, left, upward or downward we have:
By knowing this things, we can solve our problem as follows:
FIRST.
- Translating <em>11 units to the left:</em>
- Then translating<em> 5 units down:</em>
Since the new function is fatter, the factor we need to multiply the term <em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.
<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>
SECOND.
- Translating <em>8 units to the right:</em>
- Then translating<em> 1 unit down:</em>
As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.
<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>