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2 years ago

Pls help asap!! pic is shown

Mathematics

1 answer:

dsp732 years ago

3 0

The points (-5, 1), (-2, 4), (2, 4), and (-5, 1) gives the piecewise defined function as the second option;

g(x) = x + 6, when x < -2

g(x) = x², when -2 ≤ x < 2

g(x) = 6 - x, when x ≥ 2

<h3>How can the correct piecewise defined function be found?</h3>

Parts of the function are:

x < -2

Slope = (4-1)/(-2-(-5)) = 1

Equation is: g(x) - 4 = x - (-2)

g(x) - 4 = x + 2

g(x) = x + 2 + 4 = x + 6

g(x) = x + 6

In the region, -2 ≤ x < 2, points on the graph are;

(-2, 4), (0, 0), (2, 4)

The above points corresponds with the function;

g(x) = x²

In the region x ≥ 2, we have;

Slope = -1

Equation is: g(x) - 4 = -1×(x - 2) = 2 - x

Therefore;

g(x) = 4+2 - x = 6 - x

g(x) = 6 - x

The rule for the piecewise defined function is therefore;

g(x) = x + 6, when x < -2
g(x) = x², when -2 ≤ x < 2
g(x) = 6 - x, when x ≥ 2

The correct option is therefore the second option;

Learn more about piecewise defined functions here:

brainly.com/question/11207865

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Read 2 more answers

Which inequality represents the sentence below? The difference of a number and one and four tenths is more than nine and seventy

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The inequality represents the sentence below is that the p minus 1. 4 greater-than 9.

<h3>What is the inequality equation?</h3>

Inequality equation is the equation in which the two expressions are compared with greater than, less than or other inequality signs.

Given that the difference of a number and one and four tenths is more than nine and seventy-eight hundredths.

Before solving it, first let's discuss the tenth and hundredths,

Tenth is written as the fractional part of the number 10. The value of one tenth is equal to 1/10 or 0.1.
Hundredths is written as the fractional part of the number 100. The value of one hundredth is equal to 1/100 or 0.01.

Here, the sentence given that the difference of a number and one and four tenths is more than nine and seventy-eight hundredths.

One and four tenths can be written as,

$1\dfrac{4}{10}$

Nine and seventy-eight hundredths can be written as,

$9\dfrac{78}{100}$

Let suppose the number is <em>p</em>. This difference of this number and one four tenths is more than nine and seventy-eight hundredths. Thus,

$p-1\dfrac{4}{10} > 9\dfrac{78}{100}\\p-\dfrac{14}{10} > \dfrac{978}{100}\\p-1.4 > 9.78\\$