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Graph
p(x) using the graphs of
f(x) and
g(x) that are shown in the graph.

$4$ . Graph $p(x)$ using the graphs of $f(x)$ and $g(x)$ that are shown in the graph.

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Evaluate rational exponents

Full solution

Q.

4

. Graph

p(x)

using the graphs of

f(x)

and

g(x)

that are shown in the graph.

Understand Relationship: Understand the relationship between $p(x)$ , $f(x)$ , and $g(x)$ . Assume $p(x) = f(x) + g(x)$ based on typical operations used in combining functions.
Identify Key Points: Identify key points from the graphs of $f(x)$ and $g(x)$ . For example, if $f(x) = x^2$ and $g(x) = x$ , at $x = 1$ , $f(1) = 1^2 = 1$ and $g(1) = 1$ .
Calculate $p(x)$ : Calculate $p(x)$ at specific $x$ values using the assumed relationship. $\newline$ At $x = 1$ , $p(1) = f(1) + g(1) = 1 + 1 = 2$ .
Plot Calculated Points: Plot the calculated points for $p(x)$ on the graph. $\newline$ Mark the point $(1, 2)$ on the graph.
Draw Graph: Draw the graph of $p(x)$ by connecting the plotted points smoothly. $\newline$ Ensure the graph shape makes sense based on the operations used (adding in this case).

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\newline

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(A) The limit exists, and we found it!

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(B) The limit doesn't exist (probably an asymptote).

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