What is a vertical stretch on a graph?

What is a vertical stretch on a graph?

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 tell if a graph is vertically stretched?

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 horizontal stretch the same as a vertical compression?

With a parabola whose vertex is at the origin, a horizontal stretch and a vertical compression look the same.

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.

How do you know if its a vertical stretch or shrink?

Key Takeaways

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

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 – ).

What is a vertical compression by a factor of 2?

The graph of g(x)=12×2 g ( x ) = 1 2 x 2 is compressed vertically by a factor of 2; each point is half as far from the x -axis as its counterpart on the graph of y=x2.

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.

What is a vertical compression example?

Vertical compressions occur when a function is multiplied by a rational scale factor. The base of the function’s graph remains the same when a graph is compressed vertically. Let’s apply the concept to compress f(x) = 6|x| + 8 by a scale factor of 1/2. To compress f(x), we’ll multiply the output value by 1/2.

What is a vertical compression by a factor of 2 3?

(1) A vertical compression of 2/3 is achieved by multiplying the function by 2/3. This reduces the amplitude by a factor of 2/3. Thus the leading coefficient is 2/3. (2) A reflection in the x-axis is achieved by multiplying f(x) by -1.

What is a vertical compression by a factor of 1 3?

When you compress it vertically, it is the same as stretching it horizontally. When you stretch a function horizontally, the f(x) values get smaller and smaller. So to make f(x) smaller, multiply the function by (1/3).

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

Stretch and Shrink A function’s graph is vertically stretched or shrunk by multiplying the function rule by some constant a>0: g(x)=a⋅f(x). All vertical distances from the graph to the x-axis are changed by the factor a. Thus, preserving any x-intercepts.

How do you find the vertical and horizontal asymptotes?

The vertical asymptotes will occur at those values of x for which the denominator is equal to zero: x2 − 4=0 x2 = 4 x = ±2 Thus, the graph will have vertical asymptotes at x = 2 and x = −2. To find the horizontal asymptote, we note that the degree of the numerator is one and the degree of the denominator is two.

How do you find a vertical asymptote?

Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value). Find the asymptotes for the function . The graph has a vertical asymptote with the equation x = 1.

How do you determine the domain and range of a rational function?

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. A rational function is a function of the form f(x)=p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0 .

How do you transform a rational function?

Any graph of a rational function can be obtained from the reciprocal function f(x)=1x f ( x ) = 1 x by a combination of transformations including a translation, stretches and compressions.

What is a rational parent function?

The parent function of a rational function is f(x)=1x and the graph is a hyperbola . The domain and range is the set of all real numbers except 0 . Domain:{x | x≠0}Range:{y | y≠0} Excluded value. In a rational function, an excluded value is any x -value that makes the function value y undefined.

How do you solve a rational function by graphing?

Process for Graphing a Rational Function

  1. Find the intercepts, if there are any.
  2. Find the vertical asymptotes by setting the denominator equal to zero and solving.
  3. Find the horizontal asymptote, if it exists, using the fact above.
  4. The vertical asymptotes will divide the number line into regions.
  5. Sketch the graph.

Is a reciprocal function continuous?

Is a reciprocal function continuous? A function is not continuous at any point not in its domain. Hence your reciprocal function is continuous at every value of x other than x=0, where it is discontinuous.

What is the reciprocal of a function?

The reciprocal function of a function f(x) is 1/f(x). The general form of a reciprocal function is r(x) = a / (x – h) + k. The vertical asymptote of r(x) is x = h. The horizontal asymptote of r(x) is y = k.