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4 votes
Compare the functions shown below:

g(x)
f(x) = −6x − 3 cosine function with y intercept at 0, negative 3 h(x) = 2 cos(x + π) − 1


Using complete sentences, explain which function has the greatest y-intercept.

Compare the functions shown below: g(x) f(x) = −6x − 3 cosine function with y intercept-example-1
User Taisha
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4.5k points

2 Answers

10 votes

Both functions have the same y-intercepts.

  • y = -3
User Ali Seyedi
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4.9k points
1 vote

All functions have the same y-intercept of
\( -3 \), and none has a greater y-intercept than the others based on the information provided.

To determine which function has the greatest y-intercept, we need to evaluate the y-intercept for each given function. The y-intercept of a function is the value of the function when
\( x = 0 \).

For
\( f(x) = -6x - 3 \):

The y-intercept can be found by setting
\( x = 0 \):


\( f(0) = -6(0) - 3 = -3 \)

So, the y-intercept for
\( f(x) \) is
\( -3 \).

For
\( h(x) = 2 \cos(x + \pi) - 1 \):

The y-intercept can be found by setting
\( x = 0 \):


\( h(0) = 2 \cos(0 + \pi) - 1 = 2 \cos(\pi) - 1 = 2(-1) - 1 = -2 - 1 = -3 \)

So, the y-intercept for
\( h(x) \) is
\( -3 \)\( -3 \).

Since both functions have the same y-intercept of
\( -3 \), neither function has a greater y-intercept than the other; they are equal.

The function \( g(x) \) is not given explicitly, but if we assume it is the cosine function graphed in the image with a y-intercept at
\( (0, -3) \), then it would also have a y-intercept of
\( -3 \), the same as the other two functions.

Therefore, all functions have the same y-intercept of
\( -3 \), and none has a greater y-intercept than the others based on the information provided.

User Mumtaz
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3.7k points