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If p(x)=∣2∣ and t(x)=−x−3, how will the graph of t(x) be different from the graph of p(x)?

a) Inverted and then shifted 5 units up.

b) Inverted and then shifted 5 units down.

c) Inverted and then shifted 3 units up.

d) Inverted and then shifted 3 units down.

1 Answer

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Final answer:

The main difference is that t(x) is an inverted version of p(x) due to its negative slope and is shifted 3 units down because of its y-intercept of -3.

Step-by-step explanation:

The student's question asks about the differences between the graph of p(x)=|2| and t(x)=-x-3. The graph of p(x) is simply a horizontal line at the value of 2 since the absolute value of 2 is always 2, regardless of the value of x. On the other hand, the graph of t(x)=-x-3 is a linear equation with a negative slope and a y-intercept of -3.

Comparing the two, we see that the graph of t(x) is inverted relative to p(x) because of the negative coefficient in front of the x, which implies a downward slope. Additionally, t(x) experiences a vertical shift compared to p(x), specifically shifted down by 3 units due to the -3 intercept.

The correct answer to how the graph of t(x) will be different from the graph of p(x) is (d) Inverted and then shifted 3 units down.

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