Graph the piecewise functionshow how you got the function
1 answer:
(4). If we break down this piecewise function, we have 3 main expressions to deal with, 'h(x) = 5 if {x ≥ 4}' (represented by the green graph) 'h(x) = x if {0 ≤ x ≤ 4}' (represented by the blue graph) and 'h(x) = 1 / 2x + 2 if {x < 0}' (represented by the red graph).
Take a look at the attachment below for your graph of these 3 functions / expressions.
(5). For this part we want to determine the average rate of change of the function f(x) = 4x² - 5x - 8 over the interval [- 2,3]. Remember that to calculate average rate of change between the 2 points we use the following formula...
f(b) - f(a) / b - a,
f(3) = 4(3)² - 5(3) - 8 = 4(9) - 15 - 8 = 36 - 15 - 8 = 13,
f(- 2) = 4(- 2)² - 5(- 2) - 8 = 4(4) + 10 - 8 = 16 + 10 - 8 = 18
13 - 18 / 3 - (- 2) = - 5 / 5 = - 1
Therefore the average rate of change of the function f(x) = 4x² - 5x - 8 over the interval [- 2,3] will be - 1.
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Answer:
Step-by-step explanation:
The vertical asymptotes need to be in the denominator. They become VA's when that small expression value equals zero.
x=-2 will become (x+2)
and x=-6 will become (x+6)
The x intercepts will be in the numerator.
x=-1 will go with (x+1) and x=3 will go with (x-3)
The horizontal A must be the quotient of the coefficient of the numerator and denominator, since both the top and bottom have the same power.
To make the quotient 7, we place a seven in the numerator so 7/1=7.
First, we are going to multiply the pieces of wood by the length of each piece to find the total length she will need:
Next, we are going to convert 2262 centimeters to meters. To do that we are going to take advantage of the fact that 1 m=100cm:
Now, we just need to divide the total length of wood Marguerite needs by the length of each board of wood:
Since she will need full boards of wood, we must round 3.77 to its nearest integer 4.
We can conclude that <span>Marguerite will need 4 boards of wood.</span>
Next, we are going to convert 2262 centimeters to meters. To do that we are going to take advantage of the fact that 1 m=100cm:
Now, we just need to divide the total length of wood Marguerite needs by the length of each board of wood:
Since she will need full boards of wood, we must round 3.77 to its nearest integer 4.
We can conclude that <span>Marguerite will need 4 boards of wood.</span>
Answer:
The solution is:
Please check the attached line graph below.
Step-by-step explanation:
Given the expression
Add 4 to both sides
Simplify
Subtract 4r from both sides
Simplify
Multiply both sides by -1 (reverses the inequality)
Simplify
Divide both sides by 11
Simplify
Therefore, the solution is:
Please check the attached line graph below.
