Find an equation of cosine function with maximum of 7, minimum of -7 and period of 7
1 answer:
Answer:
<u>Step-by-step explanation:</u>
y = A cos (Bx - C) + D
- A = amplitude (vertical stretch)
- Period = 2π/B
- C/B = phase shift
- D = vertical shift
The minimum is -7 and the max is 7 so A = 7 and D = 0
Period is 7. Since P = 2π/B then 7 = 2π/B --> B = 2π/7
Nothing was stated about a phase shift so you can use any value for C. I chose C = 0.
Now, input A = 7, B = 2π/7, C = 0, & D = 0 into the equation
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The third graph or bottom left graph represents
Step-by-step explanation:
Step 1:
To determine which of the given graphs represents the equation , we substitute some values in the place of x.
When
Anything with an exponent of 0 will equal 1.
So the graphs on the right side cannot be the answers.
Step 2:
Now we substitute another value to determine which graph represents
When
The value of f(x) when is lesser than the value of f(x) when
So the third graph or bottom left graph represents
Answer:
yes
Step-by-step explanation:
There are several ways to go at this.
My first choice is to use a graphing calculator. It shows the function has a zero at x=5, so x-5 is a factor.
Another good choice is to use synthetic division (2nd attachment). If the remainder is zero, then x-5 is a factor. It is and it is.
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You can also evaluate the function at x=5. The remainder theorem tells you that if the value is zero, then x-5 is a factor. Evaluating the polynomial written in Horner form is a lot like synthetic division.
(((x -4)x -15)x +58)x -40 for x=5 is ... (-10·5 +58)5 -40 = 40-40 = 0
The value of h(5) is zero, so x-5 is a factor of h(x).
