10pts

compare the following functions:

f(x) = −4sin(x − 0.5) + 11 g(x)

graph of a quadratic with points at 2, 7 and 3, 6 and 4, 7 h(x)

x y

−2 14

−1 9

0 6

1 5

2 6

3 9

4 14

which function has the smallest minimum?

all three functions have the same minimum

f(x)

g(x)

h(x)

Hence the function which has the smallest minimum is: h(x)

Step-by-step explanation:

We are given function f(x) as:

We know that the minimum value attained by the sine function is -1 and the maximum value attained by sine function is 1.

so the function f(x) receives the minimum value when sine function attains the maximum value since the term of sine function is subtracted.

Hence, the minimum value of f(x) is: 11-4=7 ( when sine function is equal to 1)

x    y

−2   14

−1   9

 0   6

  1   5

 2   6

 3   9

 4   14

Hence, the minimum value attained by h(x) is 5. ( when x=1)

so, the equation will be:

Hence on putting these coordinates we will get:

a=1,b=3 and c=7.

Hence the function g(x) is given as:

So,the minimum value attained by g(x) could be seen from the graph is at the point (3,6).

Hence, the minimum value attained by g(x) is 6.

Hence the function which has the smallest minimum is h(x)

no this is a nonlinear negative

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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