Answer:
Refer below.
Step-by-step explanation:
To graph the given functions f(x) = x² and g(x) = x² + 8 in the same rectangular coordinate system, we will start by selecting integers for 'x' from -2 to 2. Then, we'll plot the points for both functions and analyze how the graph of 'g' is related to the graph of 'f'.
Step 1: Create a table of values for f(x) and g(x). Do this by plugging in x = -2 until you reach x = 2.
[tex]\begin{tabular}{|c|c|}\cline{1-2}\( x \) & \( f(x) = x^2 \) \\\cline{1-2}-2 & 4 \\\cline{1-2}-1 & 1 \\\cline{1-2}0 & 0 \\\cline{1-2}1 & 1 \\\cline{1-2}2 & 4 \\\cline{1-2}\end{tabular}[/tex]
[tex]\begin{tabular}{|c|c|}\cline{1-2}\( x \) & \( g(x) = x^2 + 8 \) \\\cline{1-2}-2 & 12 \\\cline{1-2}-1 & 9 \\\cline{1-2}0 & 8 \\\cline{1-2}1 & 9 \\\cline{1-2}2 & 12 \\\cline{1-2}\end{tabular}[/tex]
Step 2: Plot the points on the same coordinate system. I've attached an image for you to view.
Step 3: Analyze the graphs.
Notice the graph of g(x) = x² + 8 is a vertical shift of the graph of f(x) = x². Specifically, the entire graph of f(x) is shifted 8 units upwards to obtain the graph of g(x). This means every point on the graph of f(x) is moved up by 8 units to get the corresponding point on the graph of g(x).
