Pr3inahwalcamir
Answered

Compare the functions shown below:

f(x) = 2 sin (3x + π) − 2

g(x) = (x − 3)2 − 1

h(x)


x y

-2 3

-1 -2

0 -5

1 -6

2 -5

3 -2

4 3

Which function has the smallest minimum y-value?

Verified Answer :

nobillionaireNobley

f(x) = 2 sin (3x + pi) - 2 has the minimum y-value of -4

g(x) = (x - 3)^2 - 1 has a minimum y-value of -1

h(x) has the minimum y-value of -6

Therefore, h(x) has the smallest minimum y-value.

The correct answer is:


h(x)


Explanation:


Graphing f(x) and tracing the function, we find the smallest y-value to be -4.


We can use the form of the equation for g(x). It is in vertex form, which is

g(x) = a(x-h)²+k, where (h, k) is the vertex.


In our function, g(x) = (x-3)²-1, we have a vertex of (3, -1). The vertex of a quadratic function is either the maximum or minimum. Since the value of a would be 1, the graph would open upward; thus the vertex would be a minimum, and -1 would be the minimum y-value.


We can see from the table that the smallest y-value in h(x) is -6. This is smaller than the other two, so this is the smallest.

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