Question: What Does A Vertical Shrink Look Like?

How do you do 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..

What is a vertical shift?

Vertical shifts are outside changes that affect the output ( y- ) axis values and shift the function up or down. … Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

What does vertically stretched by a factor of 2 mean?

Stretching f(x) vertically by a factor of 2 will result in h(x) being equal to 2 times f(x). Stretching f(x) vertically by a factor of 3 will result to h(x) being equal to 3 times f(x).

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 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 tell if it is a vertical stretch or shrink?

Key Points 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 ) .

How do you find the domain?

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

How do you tell 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.

Is a vertical stretch 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.

What is vertical shift in Precalc?

Vertical shifts are outside changes that affect the output ( y- ) axis values and shift the function up or down. … Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

What is the phase shift?

The Phase Shift is how far the function is shifted horizontally from the usual position. The Vertical Shift is how far the function is shifted vertically from the usual position.

How do you tell if a graph is a function?

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

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 vertically stretch a graph?

How To: Given a function, graph its vertical stretch.Identify the value of a.Multiply all range values by a.If a > 1 \displaystyle a>1 a>1, the graph is stretched by a factor of a. If 0 < a < 1 \displaystyle { 0 }<{ a }<{ 1 } 0

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.

What does a vertical stretch affect?

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 vertically stretch a quadratic equation?

When we multiply a function by a constant, A, the effect is to scale (expand or shrink) the graph vertically. If A > 1, the function is stretched vertically. If A < 1 it is compressed vertically, and if A is negative, it still scales the graph by |A|, but it is also flipped across the x-axis.

How do you identify the domain and range of a function?

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.