Answer: the graph of y = x² - 4 is a U-shaped curve, while the graph of y = x is a straight line. If we graph the function y = x + 7, it would also be a straight line but shifted upwards by 7 units
Explanation:
The given function is y = x² - 4. Let's plot the points on the graph.
x | y
-3 | 5
-2 | 0
-1 | -3
0 | -4
1 | -3
2 | 0
3 | 5
When we plot these points, we get a U-shaped graph that opens upward. The vertex of the graph is at (0, -4), and the graph is symmetrical around the y-axis.
Now, let's compare this graph to the function y = x. The function y = x represents a straight line with a slope of 1 passing through the origin (0, 0). It has a positive slope, meaning the line goes up as x increases.
The key difference between the two graphs is that the graph of y = x² - 4 is a curve, while the graph of y = x is a straight line. The curve is a result of the squared term in the function.
Now, let's make a prediction about the function y = x + 7.
Since this function has a slope of 1, just like y = x, the graph of y = x + 7 would also be a straight line. However, the graph would be shifted vertically upwards by 7 units. The line would still have a positive slope and pass through the point (0, 7) instead of the origin (0, 0).
In summary, the graph of y = x² - 4 is a U-shaped curve, while the graph of y = x is a straight line. If we graph the function y = x + 7, it would also be a straight line but shifted upwards by 7 units.