Quick Answer: What Is The Difference Between Vertical Stretch And Horizontal Compression?

How do you do a vertical stretch 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 vertically stretch a linear function?

Graphing a Linear Function Using TransformationsAnother option for graphing is to use transformations of the identity function f(x)=x f ( x ) = x . … In the equation f(x)=mx f ( x ) = m x , the m is acting as the vertical stretch or compression of the identity function.More items…

How do you vertically compress a function?

In general, if y = F(x) is the original function, then you can vertically stretch or compress that function by multiplying it by some number a: If a > 1, then aF(x) is stretched vertically by a factor of a. For example, if you multiply the function by 2, then each new y-value is twice as high.

What is a horizontal shift?

Horizontal shifts are inside changes that affect the input ( x- ) axis values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

What is vertical stretch and shrink?

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 tell if a graph is horizontally stretched or compressed?

If a > 1 \displaystyle a>1 a>1, then the graph will be stretched.If 0 < a < 1, then the graph will be compressed.If a < 0 \displaystyle a<0 a<0, then there will be combination of a vertical stretch or compression with reflection.

What does a horizontal stretch look like?

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).

How do you know if it’s a horizontal or vertical stretch?

Key Points If b>1 , the graph stretches with respect to the y -axis, or vertically. If b<1 , the graph shrinks with respect to y -axis. in general, a horizontal stretch is given by equation f(cx) f (c x ) .

What are the 7 parent functions?

The following figures show the graphs of parent functions: linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent.

What is the difference between vertical stretch and 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 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.

How do you horizontally stretch an absolute value function?

Absolute Value FunctionsThe absolute value parent function, written as f(x)=| x |, is defined as.To translate the absolute value function f(x)=| x | vertically, you can use the function.g(x)=f(x)+k.To translate the absolute value function f(x)=| x | horizontally, you can use the function.g(x)=f(x−h).More items…

How do you shift a function horizontally?

A General Note: Horizontal Shift Given a function f, a new function g ( x ) = f ( x − h ) \displaystyle g\left(x\right)=f\left(x-h\right) g(x)=f(x−h), where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift right. If h is negative, the graph will shift left.

What does a vertical shrink look like?

The y -values are being multiplied by a number between 0 and 1 , so they move closer to the x -axis. This tends to make the graph flatter, and is called a vertical shrink. In both cases, a point (a,b) on the graph of y=f(x) y = f ( x ) moves to a point (a,kb) ( a , k b ) on the graph of y=kf(x) y = k f ( x ) .

How do you find a horizontal asymptote?

To find horizontal asymptotes:If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.More items…•

How do you find the vertical stretch of a rational function?

Given a simple rational function, f, and a new function g such that , then: Ø If , then the graph of g is a vertical stretch of the graph of f by a factor of c. Ø If , then the graph of g is a vertical compression of the graph of f by a factor of c.

How do you know if a function is even or odd?

You may be asked to “determine algebraically” whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even.