Asked by SM
Describe the transformation of f(x) = x² represented by g (x) = (x - 1)² - 2. Then identify the graph of each function
The graph of g is a translation _____________ and _____________ of the graph of f.
Answer choices
⬇️
1 Unit left, 1 Unit right, 1 Unit up, 1 Unit down,
2 units left, 2 units right, 2 units up, 2 units down
The graph of g is a translation _____________ and _____________ of the graph of f.
Answer choices
⬇️
1 Unit left, 1 Unit right, 1 Unit up, 1 Unit down,
2 units left, 2 units right, 2 units up, 2 units down
Answers
Answered by
GPT-4o mini
To analyze the transformation of the function \( f(x) = x^2 \) to \( g(x) = (x - 1)^2 - 2 \), we can break it down step by step.
1. **Starting function**: \( f(x) = x^2 \)
- This is a parabola that opens upwards with the vertex at (0, 0).
2. **Step 1 - Horizontal Translation**: \( (x - 1)^2 \)
- The expression \( (x - 1) \) indicates a horizontal translation of the graph to the right by 1 unit.
- So, after this step, the vertex of the parabola moves from (0, 0) to (1, 0).
3. **Step 2 - Vertical Translation**: \(-2\)
- The subtraction of 2 in \(-2\) indicates a vertical translation downwards by 2 units.
- Thus, the vertex moves from (1, 0) to (1, -2).
Putting these transformations together, the graph of \( g(x) = (x - 1)^2 - 2 \) is obtained by first shifting the graph of \( f(x) = x^2 \) to the right by 1 unit and then down by 2 units.
So, the final answer to the fill-in-the-blank statement is:
The graph of \( g \) is a translation **1 unit right** and **2 units down** of the graph of \( f \).
1. **Starting function**: \( f(x) = x^2 \)
- This is a parabola that opens upwards with the vertex at (0, 0).
2. **Step 1 - Horizontal Translation**: \( (x - 1)^2 \)
- The expression \( (x - 1) \) indicates a horizontal translation of the graph to the right by 1 unit.
- So, after this step, the vertex of the parabola moves from (0, 0) to (1, 0).
3. **Step 2 - Vertical Translation**: \(-2\)
- The subtraction of 2 in \(-2\) indicates a vertical translation downwards by 2 units.
- Thus, the vertex moves from (1, 0) to (1, -2).
Putting these transformations together, the graph of \( g(x) = (x - 1)^2 - 2 \) is obtained by first shifting the graph of \( f(x) = x^2 \) to the right by 1 unit and then down by 2 units.
So, the final answer to the fill-in-the-blank statement is:
The graph of \( g \) is a translation **1 unit right** and **2 units down** of the graph of \( f \).