- What are the 7 parent functions?
- What does F 2x mean?
- How do you compress a vertical equation?
- How do you know if its a vertical stretch or compression?
- Is a vertical stretch positive or negative?
- How do you stretch a linear function?
- What does a horizontal stretch look like?
- How do you tell if a graph is horizontally stretched or compressed?
- What is a vertical stretch by a factor of 2?
- How do you do a vertical stretch by a factor of 3?
- How do you horizontally stretch an absolute value function?
- How do you vertically stretch a log?
- How do you find a horizontal asymptote?
- What is a horizontal shift?
- How do you find the vertical shift?
- What are the 4 types of transformations?
- What is vertical stretch and shrink?
- How do you find vertical translation?

## 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.