When Stretching By Factor Of 3 What Does That Mean? (Solution)

If g(x) = 3f (x): For any given input, the output iof g is three times the output of f, so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.

Can a function be stretched by a factor of 3?

• To attain y = |x/3|, we stretch the parent function y = |x| by a factor of 3. The graph shown above confirms this, and we can apply the same process when horizontally stretching the graphs of other functions. Ready to graph more functions and apply horizontal stretches?

What is a vertical stretch factor of 3?

Stretching f(x) vertically by a factor of 3 will result to h(x) being equal to 3 times f(x). Hence, h(x) = 3|x|.

What does stretch by a factor mean?

A horizontal stretch or shrink by a factor of 1/k means that the point (x, y) on the graph of f(x) is transformed to the point (x/k, y) on the graph of g(x).

What is a horizontal stretch by a factor of 2?

The graph of y=(0.5x)2 y = ( 0.5 x ) 2 is a horizontal stretch of the graph of the function y=x2 y = x 2 by a factor of 2. The graph of y=(2x)2 y = ( 2 x ) 2 is a horizontal compression of the graph of the function y=x2 y = x 2 by a factor of 2.

How do you calculate stretch factor?

1 Answer

1. Refer to: y=af(b(x−h))+k.
2. A vertical stretch is the stretching of a function on the x-axis.
3. A horizontal stretch is the stretching of a function on the y-axis.
4. For example:
5. b=12.
6. To vertically stretch we use this formula:
7. To horizontally stretch we use this formula:
8. x1=x12.

How do you stretch a horizontal by a factor of 3?

If g(x) = 3f (x): For any given input, the output iof g is three times the output of f, so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.

What is vertical stretch factor?

The vertical stretch of a graph measures the stretching or shrinking factor in the vertical direction. For example, if a function increases three times as fast as its parent function, it has a stretch factor of 3. If the graph has a single vertex and a strictly increasing slope, it is most likely a parabola.

What is a vertical compression by a factor of 1 3?

Say if you have an absolute value function f(x)= |4-x|, the way you would vertically compress it is by affecting it’s slope. If you multiply the number in front of x by 1 1/3 or 1.3333 repeating. The 1 aspect of 1 and 1/3 helps the slope stay constant, the 1/3 or. 3333 repeating compresses it vertically by 1/3.

What does stretching a graph mean?

When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.

How is a stretch different from a dilation?

A reduction (think shrinking) is a dilation that creates a smaller image, and an enlargement (think stretch) is a dilation that creates a larger image. If the scale factor is between 0 and 1 the image is a reduction. If the scale factor is greater than 1, the image is an enlargement.

What is a horizontal stretch?

A horizontal stretching is the stretching of the graph away from the y-axis. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis. • if k > 1, the graph of y = f (k•x) is the graph of f (x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k.

How do you describe a horizontal stretch?

Key Takeaways

1. When by either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.
2. In general, a vertical stretch is given by the equation y=bf(x) y = b f ( x ).
3. In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ).

What does 2f A mean?

2f(a) is two times the value of f applied at a. For example, if f(x) = x^2, then f(2a) = (2a)^2 = 4a^2, and 2f(a) = 2a^2.