What Is Stretching A Graph Vertically And Horizontally? (Correct answer)

vertical stretching/shrinking changes the y -values of points; transformations that affect the y -values are intuitive. horizontal stretching/shrinking changes the x -values of points; transformations that affect the x -values are counter-intuitive.

How do you stretch a graph?

• To stretch or shrink the graph in the x direction, divide or multiply the input by a constant. As in translating, when we change the input, the function changes to compensate. Thus, dividing the input by a constant stretches the function in the x direction, and multiplying the input by a constant shrinks the function in the x direction.

What does it mean to stretch a graph horizontally?

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 does it mean when a graph is stretched vertically?

What is a vertical stretch? Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. This results in the graph being pulled outward but retaining the input values (or x). When a function is vertically stretched, we expect its graph’s y values to be farther from the x-axis.

How do you know if it is a horizontal or vertical stretch or 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 vertically stretch a graph?

To stretch or shrink the graph in the y direction, multiply or divide the output by a constant. 2f (x) is stretched in the y direction by a factor of 2, and f (x) is shrunk in the y direction by a factor of 2 (or stretched by a factor of ). Here are the graphs of y = f (x), y = 2f (x), and y = x.

What is vertical and horizontal?

In geometry, we use the words vertical and horizontal for standing and sleeping respectively. Anything parallel to the horizon is called horizontal. As vertical is the opposite of horizontal, anything that makes a 90-degree angle (right angle) with the horizontal or the horizon is called vertical.

How does a graph stretch?

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.

What is a stretch and shrink of graphs?

What are Vertical Stretches and Shrinks? While translations move the x and y intercepts of a base graph, stretches and shrinks effectively pull the base graph outward or compress the base graph inward, changing the overall dimensions of the base graph without altering its shape.

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 ).

What’s the difference between vertical and horizontal?

A vertical line is any line parallel to the vertical direction. A horizontal line is any line normal to a vertical line. Horizontal lines do not cross each other.

What is stretch math?

stretch. A stretch or compression is a function transformation that makes a graph narrower or wider. stretching. Stretching a graph means to make the graph narrower or wider.

How do you translate a graph vertically?

Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated k units vertically by moving each point on the graph k units vertically. g (x) = f (x) + k; can be sketched by shifting f (x) k units vertically.

How do you move a graph vertically and horizontally?

The vertical shift results from a constant added to the output. Move the graph up for a positive constant and down for a negative constant. The horizontal shift results from a constant added to the input. Move the graph left for a positive constant and right for a negative constant.

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.