Math  /  Algebra

QuestionGraph the following function by starting with the graph of y=x2y=x^{2} and using transformations (shifting, compressing, stretching, and/or reflection). f(x)=23x2f(x)=\frac{2}{3} x^{2}

Studdy Solution

STEP 1

1. The base function is y=x2 y = x^2 .
2. The function f(x)=23x2 f(x) = \frac{2}{3} x^2 is a transformation of the base function.
3. Transformations include vertical stretching, compressing, and shifting.

STEP 2

1. Identify the base function and its graph.
2. Determine the transformation applied to the base function.
3. Apply the transformation to graph the new function.

STEP 3

The base function is y=x2 y = x^2 , which is a standard parabola opening upwards with its vertex at the origin (0,0)(0, 0).

STEP 4

The function f(x)=23x2 f(x) = \frac{2}{3} x^2 involves a vertical compression of the base function.

STEP 5

The coefficient 23\frac{2}{3} indicates that the parabola is compressed vertically by a factor of 23\frac{2}{3}.

STEP 6

To graph f(x)=23x2 f(x) = \frac{2}{3} x^2 , start with the graph of y=x2 y = x^2 and compress it vertically by multiplying the y y -values of each point by 23\frac{2}{3}.
The graph of f(x)=23x2 f(x) = \frac{2}{3} x^2 is a vertically compressed parabola compared to the graph of y=x2 y = x^2 .

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