Question

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Answer 1

[AI-generated answer — Bot GPT 3.5]

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Answer 2

Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ?(1 point)

Responses

(0,−2)
left parenthesis 0 comma negative 2 right parenthesis

(−1,−5)
left parenthesis negative 1 comma negative 5 right parenthesis

(1,2)
left parenthesis 1 comma 2 right parenthesis

(−1,−3)

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the point on the graph described by the function \(y = (2x+1)^2 - 4\), we substitute the given x-values into the function and solve for y.

Let's check each of the options:
1. For (0, -2):
When x = 0,
\(y = (2(0) + 1)^2 - 4\)
\(y = (1)^2 - 4\)
\(y = 1 - 4\)
\(y = -3\), not -2. So, (0, -2) is not on the graph.

2. For (-1, -5):
When x = -1,
\(y = (2(-1) + 1)^2 - 4\)
\(y = (-1)^2 - 4\)
\(y = 1 - 4\)
\(y = -3\), not -5. So, (-1, -5) is not on the graph.

3. For (1, 2):
When x = 1,
\(y = (2(1) + 1)^2 - 4\)
\(y = (2 + 1)^2 - 4\)
\(y = (3)^2 - 4\)
\(y = 9 - 4\)
\(y = 5\)
So, (1, 2) is a point on the graph.

4. For (-1, -3):
When x = -1,
\(y = (2(-1) + 1)^2 - 4\)
\(y = (-2 + 1)^2 - 4\)
\(y = (-1)^2 - 4\)
\(y = 1 - 4\)
\(y = -3\)
So, (-1, -3) is a point on the graph.

Therefore, the correct point on the graph as described by the function is (-1, -3).

Answer 4

Use the image to answer the question.

A line graph shows months of the year versus average rainfall. The x-axis represents month of the year, ranging from January to December. The y-axis shows the average rainfall in inches ranging from 0 to 4 in increments of 1. A curve is plotted on the graph that passes through the following approximate points left parenthesis January comma 2.3 right parenthesis, left parenthesis February comma 2 right parenthesis, left parenthesis March comma 2 right parenthesis, left parenthesis April comma 0.6 right parenthesis, left parenthesis May comma 0.6 right parenthesis, June comma 0.2 right parenthesis, left parenthesis July comma 0.45 right parenthesis, left parenthesis August comma 0.55 right parenthesis, left parenthesis September comma 0.7 right parenthesis, left parenthesis October comma 1.6 right parenthesis, left parenthesis November comma 2.4 right parenthesis, and left parenthesis December comma 3.2 right parenthesis.

Which of the following are the two quantities whose functional relationship is described in the given graph?

(1 point)
Responses

The two quantities are the x-values and the y-values.
The two quantities are the x -values and the y -values.

The two quantities are inches and months of the year.
The two quantities are inches and months of the year.

The two quantities are the average rainfall in inches and the month of the year.
The two quantities are the average rainfall in inches and the month of the year.

The two quantities are the average rainfall in inches and the years.
The two quantities are the average rainfall in inches and the years.

Answer 5

[AI-generated answer — Bot GPT 3.5]

The two quantities whose functional relationship is described in the given graph are the average rainfall in inches and the month of the year.

Therefore, the correct response is:
The two quantities are the average rainfall in inches and the month of the year.