Match the key aspect of a function's graph with its meaning

Mathematics

1 answer:

Aliun [14]3 years ago

8 0

Answer:

y- intercept --> Location on graph where input is zero

f(x) < 0 --> Intervals of the domain where the graph is below the x-axis

x- intercept --> Location on graph where output is zero

f(x) > 0 --> Intervals of the domain where the graph is above the x-axis

Step-by-step explanation:

Y-intercept: The y-intercept is equivalent to the point where x= 0. 'x' is the input variable in an equation, therefore the y-intercept is where the input, or x, is equal to 0.

f(x) <0: Notice the 'lesser than' sign. This means that the value of f(x), or 'y', is less than 0. This means that this area consists of intervals of the domain below the x-axis.

X-intercept: The x-intercept is the location of the graph where y= 0, or the output is equal to 0.

f(x) >0: In this, there is a 'greater than' sign. This means that f(x), or 'y', is greater than 0. Therefore, this consists of intervals of the domain above the x-axis.

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RSTU is a parallelogram.

KonstantinChe [14]

The answer is 95
Angles ∠UTS and ∠URS are equal = 120
The parallelogram is 360 degrees so,
360-120= 240
240 is both ∠RST and ∠RUT so divide it by 2= 120
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3 years ago

Read 2 more answers

Which ordered pair is NOT a solution to the inequality in the graph? (5,1) (4,6) (0,0) (-2,-8)

n200080 [17]

<h3>Answer: (5,1) </h3>

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Explanation:

The red shaded region is the solution set. In other words, if the point is in the red region, then it is a solution. A point like (0,0) is in the red area, so we cross that off the list. The same applies for (4,6) and (-2,-8) as well.

In contrast, a point like (5,1) is not in the red shaded area, so this point is not a solution. Hence it's the final answer.

Note: the solid boundary line means points on the boundary are considered solutions. A dashed boundary line would be used to exclude boundary points from the solution set. Solid boundary lines always go with "or equal to".

Refer to the drawing below if you need a visual of what's going on. I've plotted the four points on the graph given.

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Here's an algebraic approach if you don't have a graph and only have the inequality. Ignore this section if you prefer the first section above.

If we plugged (x,y) = (0,0) into the inequality, then we get...

$y \ge 2x-4\\\\0 \ge 2(0)-4\\\\0 \ge 0-4\\\\0 \ge -4\\\\$

That's a true statement because 0 is to the right of -4 on the number line, making 0 larger than -4. Since the last inequality is true, this makes the first inequality true. Furthermore, it algebraically confirms why (0,0) is a solution. You should find that (4,6) and (-2,-8) will lead to true statements as well, so they are solutions.

In contrast, (x,y) = (5,1) is not a solution because...

$y \ge 2x-4\\\\1 \ge 2(5)-4\\\\1 \ge 10-4\\\\1 \ge 6\\\\$

which is false. The value 1 is not larger than 6, nor is it equal to 6.

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3 years ago

Which of the following statements about the percentiles for the standard normal distribution are correct? A. The 90th percentile

shutvik [7]

Answer:

Correct option: (C) The 75th percentile is approximately 0.67

Step-by-step explanation:

The pth percentile is a data value such that at least p% of the data set is less than or equal to this data value and at least (100 - p)% of the data set are more than or equal to this data value.

If x is the pth percentile of a data set then,

P (X < x) = p/100

If $X\sim N(\mu, \sigma^{2})$ then $Z=\frac{X-\mu}{\sigma}$ , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, $Z \sim N (0, 1)$ .