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daser333 [38]
3 years ago
12

The graph of the function f(x) = (x - 3)(x + 1)

Mathematics
1 answer:
djyliett [7]3 years ago
8 0

Answer:

The graph is positive and decreasing for all real values of x where x < -1

Step-by-step explanation:

we have

f(x)=(x-3)(x+1)

The function is a vertical parabola open up

The roots (x-intercepts) are x=3 and x=-1

The vertex is the point (1,-4 ) is a minimum

using a graphing tool

see the attached figure

we know that

In the interval (-∞,-1) ---> the function is positive and decreasing

In the interval (-1,1) ---> the function is negative and decreasing

In the interval (1,3) ---> the function is negative and increasing

In the interval (3,∞) ---> the function is positive and increasing

therefore

The graph is positive and decreasing for all real values of x where x < -1

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Answer:

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Step-by-step explanation:

because

7 0
3 years ago
: Which equations have an infinite number of solutions? Select all that apply. A -2(x - 2) + 3x = x - 4 B 2x + 4(x - 1) = 3(2x +
MissTica

Option C and Option D

3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4 has infinite number of solutions

4(x + 2) + x + 1 = 2x - 3 + 3(x + 4) has infinite number of solutions

<h3><u>Solution:</u></h3>

Given that we have to find the equations that has infinite number of solutions

If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions.

If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.

<h3><u>Option A</u></h3>

-2(x - 2) + 3x = x - 4

Multiply the terms inside the bracket

-2x + 4 + 3x = x - 4

x + 4 = x - 4

Thus this equation does not have infinite number of solutions

<h3><u>Option B</u></h3>

2x + 4(x - 1) = 3(2x + 1) - 2(x - 1)

2x + 4x - 4 = 6x + 3 - 2x + 2

6x - 4 = 4x + 5

6x - 4x = 5 + 4

2x = 9

x = \frac{9}{2}

Thus this equation has only one solution.

Thus this equation does not have infinite number of solutions

<h3><u>Option C</u></h3>

3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4

3x + 2x - 4 + 6 = 4x + 6 + x - 4

5x + 2 = 5x + 2

Thus this equation has infinite number of solutions

<h3><u>Option D</u></h3>

4(x + 2) + x + 1 = 2x - 3 + 3(x + 4)

4x + 8 + x + 1 = 2x - 3 + 3x + 12

5x + 9 = 5x + 9

Thus this equation has infinite number of solutions

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