How can you tell a horizontal stretch from a vertical stretch?

Key Takeaways

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

What causes a vertical stretch or compression?

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 horizontal and vertical stretch?

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.

What is horizontal and vertical shift?

Vertical shifts are outside changes that affect the output ( y- ) axis values and shift the function up or down. Horizontal shifts are inside changes that affect the input ( x- ) axis values and shift the function left or right.

What is a vertical stretch example?

Examples of Vertical Stretches and Shrinks looks like? Using the definition of f (x), we can write y1(x) as, y1 (x) = 1/2f (x) = 1/2 ( x2 – 2) = 1/2 x2 – 1. Based on the definition of vertical shrink, the graph of y1(x) should look like the graph of f (x), vertically shrunk by a factor of 1/2.

What is the difference between a horizontal and vertical shrink?

A vertical compression (or shrinking) is the squeezing of the graph toward the x-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.

What does a vertical shrink look like?

Based on the definition of vertical shrink, the graph of y1(x) should look like the graph of f (x), vertically shrunk by a factor of 1/2. Take a look at the graphs of f (x) and y1(x). Notice that the x-intercepts have not moved.

What does a vertical stretch mean?

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 horizontal shift is vertical?

Now that we have two transformations, we can combine them together. Vertical shifts are outside changes that affect the output ( y- ) axis values and shift the function up or down. Horizontal shifts are inside changes that affect the input ( x- ) axis values and shift the function left or right.

How can you tell a horizontal stretch from a vertical stretch? Key Takeaways When by either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed. In general, a vertical stretch is given by the equation y=bf(x) y = b f ( x ) . In…