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fomenos
1 year ago
5

ANALYZE A PROBLEM Describe the x-values for which (a) f is increasing (b) f is decreasing, (c) f (x) > 0 and (d) f (x) < 0

.

Mathematics
1 answer:
Karolina [17]1 year ago
7 0

The analysis of the graph, that has x-intercepts of (0, 2), and (0, 5), we get;

a. The function increases when x > 4

b. The function decreases when x < 4

c. The function is greater than zero when x < 3, and x > 5

d. The function is less than zero when 3 < x < 5

<h3>What is a point where a function is increasing?</h3>

The location of a point where a function is increasing is where the slope of the function is larger than zero.

The description of the graph of the function are as follows;

The shape of the function  = Concave upwards

The coordinates of the vertex of the function = (4, -5)

The region where the function is decreasing is from -∞ to 4

The region where the function is decreasing is therefore; x < 4

At the vertex, (4, -5), the slope of the function is zero, therefore;

Therefore, the function is increasing where x > 4

The x-intercepts are at point (0, 3) and (0, 5)

Therefore, the function is greater than zero when x < 3, and when x > 5

The function is less than zero in the range 3 < x < 5

Learn more about the graph of functions here:

brainly.com/question/16924356

#SPJ1

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x = 1 , 7

Step-by-step explanation:

Solution:-

- The given equation is as follows:

                          y = x^2 - 8x + 7

- We can solve the above equation by either making factors or by using Quadratic formula.

Factor Approach:

- Using the constant "7" at the end of the quadratic equation we will determine two integer multiples such that their additions/subtraction results in "-8".

- So the only factor of "7" are:

                        7 x 1 = 7

                       -7 x -1 = 7

- We see that addition/subtraction of first (7 , 1 ) does not results in "-8", However, the sum of ( -1 , -7 ) = -1 - 7 = -8. So the correct factors are ( -1 , -7 ). So we replace "-8x" with our factors "-1x" and "-7x":

                       x^2 -x -7x + 7 = 0

- Take common multiples out of pair of two terms:

                        x*(x-1) -7*(x-1) = 0

                        (x-7)*(x-1) = 0

- So we equate each term in bracket with "0" and evaluate the values of x:

                        (x-7) = 0  , x = 7

                        (x-1) = 0   , x = 1

- So the solution to the quadratic equation is:

                        x = 1 , 7

               

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