How Can Horizontally Stretching The Graph Of F (x)=x3 By A Factor Of B Can Be? (Solution found)

How to calculate horizontal and vertical graph stretches?

• Horizontal And Vertical Graph Stretches And Compressions (Part 1) The general formula is given as well as a few concrete examples. y = c f(x), vertical stretch, factor of c; y = (1/c)f(x), compress vertically, factor of c; y = f(cx), compress horizontally, factor of c; y = f(x/c), stretch horizontally, factor of c; y = – f(x), reflect at x-axis

How do you stretch a graph horizontally 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.

How do you stretch a graph horizontally?

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 ).

How do you write a horizontal stretch by a factor of 2?

Thus, the equation of a function stretched vertically by a factor of 2 and then shifted 3 units up is y = 2f (x) + 3, and the equation of a function stretched horizontally by a factor of 2 and then shifted 3 units right is y = f ( (x – 3)) = f ( x – ).

How do you find the factor of a horizontal stretch?

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). Consider the following base functions, (1) f (x) = x² – 3, (2) g(x) = cos (x).

Whats a horizontal stretch?

Horizontal stretches are among the most applied transformation techniques when graphing functions, so it’s best to understand its definition. Horizontal stretches happen when a base graph is widened along the x-axis and away from the y-axis. Understanding the common parent functions we might encounter.

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 find the stretch factor of a graph?

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 do a horizontal stretch and compression?

If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x) y = f ( x ), the form y=f(bx) y = f ( b x ) results in a horizontal stretch or compression.

How do you translate a graph horizontally?

Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis. A graph is translated k units horizontally by moving each point on the graph k units horizontally. g(x) = f (x – k), can be sketched by shifting f (x) k units horizontally.

What is a horizontal shrink by 1 2?

The horizontal shrink means you shrink x by a factor of 1/2. Currently the slope on the right side of the V is 1, so to “shrink” it, you actually DIVIDE by 1/2, giving you a new slope of 2.

Why are horizontal stretches opposite?

Why are horizontal translations opposite? While translating a graph horizontally, it might occur that the procedure is opposite or counter-intuitive. That means: For negative horizontal translation, we shift the graph towards the positive x-axis.