What are the coordinates of the vertex of the graph of

1 answer:

4 0

The vertex is (3,0). The 3 inside the abs val bar tells you the x value of the vertex is 3. No number outside the abs value bar is a +0 which is the y value of the vertex.

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Please help me. I don’t understand this at all...

mylen [45]

Problem 1

With limits, you are looking to see what happens when x gets closer to some value. For example, as x gets closer to x = 2 (from the left and right side), then y is getting closer and closer to y = 1/2. Therefore the limiting value is 1/2

Another example: as x gets closer to x = 4 from the right hand side, the y value gets closer to y = 4. This y value is different if you approach x = 0 from the left side (y would approach y = 1/2)

Use examples like this and you'll get the results you see in "figure 1"

For any function values, you'll look for actual points on the graph. A point does not exist if there is an open circle. There is an open circle at x = 2 for instance, so that's why f(2) = UND. On the other hand, f(0) is defined and it is equal to 4 as the point (0,4) is on the function curve.

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Problem 2

This is basically an extension of problem 1. The same idea applies. See "figure 2" (in the attached images) for the answers.

6 0

3 years ago

Write an expression for this one <br> the sum of an odd integer and the next odd integer.

Sidana [21]

Let x is the odd integer
x +2 is the next odd integer
so sum of an odd integer and the next odd integer:
x + (x+2)

8 0

3 years ago

Sara has 20 sweets. She has 12 liquorice sweets, 5 mint sweets and 3 humbugs. Sarah is going to take, at random, two sweets Work

Debora [2.8K]

Answer:

111 / 190

Step-by-step explanation:

Let us first compute the probability of picking 2 of each sweet. Take liquorice as the first example. There are 12 / 20 liquorice now, but after picking 1 there will be 11 / 19 left. Thus the probability of getting two liquorice is demonstrated below;

$12 / 20 * 11 / 19 = \frac{33}{95},\\Probability of Drawing 2 Liquorice = \frac{33}{95}$

Apply this same concept to each of the other sweets;

$5 / 20 * 4 / 19 = \frac{1}{19},\\Probability of Drawing 2 Mint Sweets = 1 / 19\\\\3 / 20 * 2 / 19 = \frac{3}{190},\\Probability of Drawing 2 Humbugs = 3 / 190$

Now add these probabilities together to work out the probability of drawing 2 of the same sweets, and subtract this from 1 to get the probability of not drawing 2 of the same sweets;

$33 / 95 + 1 / 19 + 3 / 190 = \frac{79}{190},\\1 - \frac{79}{190} = \frac{111}{190}\\\\$