To describe how the graph of \( f(x) = x^2 \) was transformed to create the graph of \( h(x) = x^2 - 1 \), we need to analyze the relationship between these two functions.
The function \( f(x) = x^2 \) is a standard parabola that opens upwards with its vertex at the origin (0, 0).
The function \( h(x) = x^2 - 1 \) can be derived from \( f(x) = x^2 \) by applying a vertical shift.
Here's the step-by-step transformation:
1. **Vertical Shift Downward:** The graph of \( h(x) = x^2 - 1 \) is obtained by shifting the graph of \( f(x) = x^2 \) downward by 1 unit.
In general, the transformation \( g(x) = f(x) - c \) shifts the graph of \( f(x) \) downward by \( c \) units if \( c \) is positive.
So, in this case, the graph of \( f(x) = x^2 \) is transformed to the graph of \( h(x) = x^2 - 1 \) by shifting it downward by 1 unit.
Therefore, the correct answer choice is:
**The graph of \( f(x)=x^2 \) was transformed by shifting it downward by 1 unit to create the graph of \( h(x)=x^2 - 1 \).**
#6. Which answer choice describes how the graph of f(x)=x2 was transformed to create the graph of h(x)=x2−1?
1 answer