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

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 does F 2x mean?

g(x) = f(2x) is saying that g(x) is half as wide as f(x) , because for any x in g(x) , it will be the same y value as f(x) when you double x . g(x) = 1/2 f(x) is saying that g(x) is half as tall as f(x) , because for any y which is an output of f(x) , g(x) will out put a y value half as large.

How do you compress a vertical equation?

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.

How do you know if its 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.

Is a vertical stretch positive or negative?

If 0 < a < 1 you have a vertical compression and if a > 1 then you have a vertical stretching. When a is negative, then this vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.

How do you stretch a linear function?

How To: Given the equation of a linear function, use transformations to graph the linear function in the form f(x)=mx+b f ( x ) = m x + b . Graph f(x)=x f ( x ) = x . Vertically stretch or compress the graph by a factor |m|.

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 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 is a vertical 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 – ). Example: f (x) = 2×2.

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 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 vertically stretch a log?

Graphing Stretches and Compressions of y=logb(x) When the parent function f(x)=logb(x) f ( x ) = l o g b ( x ) is multiplied by a constant a > 0, the result is a vertical stretch or compression of the original graph.

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…•

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.

How do you find the vertical shift?

If you divide the C by the B (C / B), you’ll get your phase shift. The D is your vertical shift. The vertical shift of a trig function is the amount by which a trig function is transposed along the y-axis, or, in simpler terms, the amount it is shifted up or down.

What are the 4 types of transformations?

There are four main types of transformations: translation, rotation, reflection and dilation. These transformations fall into two categories: rigid transformations that do not change the shape or size of the preimage and non-rigid transformations that change the size but not the shape of the preimage.

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 find vertical translation?

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.