Question
Which graph shows the parent function f(x)=x2 horizontally compressed to form the graph of y=f(3x) ?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To visualize how the graph of the parent function \( f(x) = x^2 \) changes when it is horizontally compressed, we need to consider the transformation represented by \( y = f(3x) \).
1. The parent function \( f(x) = x^2 \) is a parabola opening upwards with its vertex at the origin (0,0).
2. The transformation \( f(3x) \) compresses the graph horizontally. Specifically, it compresses the graph by a factor of \( \frac{1}{3} \).
This means that all \( x \) values are effectively multiplied by \( \frac{1}{3} \). For example:
- The point \( (1, 1) \) on \( f(x) = x^2 \) will move to \( \left(\frac{1}{3}, 1\right) \) on \( f(3x) \).
- The point \( (-1, 1) \) will move to \( \left(-\frac{1}{3}, 1\right) \).
As a result of this transformation, the new graph of \( y = f(3x) \) appears "squeezed" horizontally compared to the original parabola.
To summarize, the graph of \( y = f(3x) \) will still be a parabola that opens upwards but will reach its values much quicker due to the horizontal compression by a factor of 3. The overall shape remains similar but is narrower. You would look for a graph that illustrates a parabola reaching its maximum more quickly in the horizontal direction.
1. The parent function \( f(x) = x^2 \) is a parabola opening upwards with its vertex at the origin (0,0).
2. The transformation \( f(3x) \) compresses the graph horizontally. Specifically, it compresses the graph by a factor of \( \frac{1}{3} \).
This means that all \( x \) values are effectively multiplied by \( \frac{1}{3} \). For example:
- The point \( (1, 1) \) on \( f(x) = x^2 \) will move to \( \left(\frac{1}{3}, 1\right) \) on \( f(3x) \).
- The point \( (-1, 1) \) will move to \( \left(-\frac{1}{3}, 1\right) \).
As a result of this transformation, the new graph of \( y = f(3x) \) appears "squeezed" horizontally compared to the original parabola.
To summarize, the graph of \( y = f(3x) \) will still be a parabola that opens upwards but will reach its values much quicker due to the horizontal compression by a factor of 3. The overall shape remains similar but is narrower. You would look for a graph that illustrates a parabola reaching its maximum more quickly in the horizontal direction.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.