i don't understand what a horizontal or vertical stretching is of a graph.
y=x^3
Find graph horizontally stretched by a factor of 4
and vertically stretched by a factor of 4
vertically? multiply it by 4 : y=4x^3
horizontally? divide x by 4
y=(x/4)^3
http://www.analyzemath.com/horizontalscaling/horizontalscaling.html
check me.
Ah, stretching graphs can be a real stretch of the imagination! Let me try to explain it in a way that's both informative and fun.
When we say a graph is horizontally stretched by a factor of 4, it means that the graph is being pulled wider, just like your favorite pair of jeans after a big holiday feast. Imagine your original graph was wearing skinny jeans, and now it's rocking some fashionable flare pants. The graph's shape remains the same, but it spreads out horizontally.
Now, when we talk about a graph being vertically stretched by a factor of 4, it's like putting that graph through a growth spurt. It's as if the graph ate its vegetables and drank its milk, resulting in a taller and more majestic appearance. Think of it as the graph standing on its tippy toes to reach new heights!
Coming back to your example, let's see what happens to the graph of y = x^3 when it's stretched horizontally by a factor of 4. The new equation would be y = (1/4)x^3. Each x-value on the graph gets multiplied by 1/4, making the graph four times wider than the original.
Similarly, when it's stretched vertically by a factor of 4, the equation becomes y = 4x^3. Now, each y-value gets multiplied by 4, making the graph quadruple in height.
I hope that explanation didn't stretch your patience too thin! Remember, graph stretching is like giving your plot a makeover with some fancy stretching exercises. Stretch on, my math-minded friend!
To understand horizontal and vertical stretching of a graph, let's start with the original equation:
y = x^3
In this equation, the independent variable x represents the input values, and the dependent variable y represents the output values or the corresponding points on the graph.
1. Horizontal Stretching:
To horizontally stretch the graph of the function by a factor of 4, we adjust the independent variable, x.
The equation for horizontally stretching is:
y = f(kx),
where k represents the stretching factor.
In this case, k = 4, so the horizontal stretching equation becomes:
y = (4x)^3
To find the graph of the function after being horizontally stretched by a factor of 4, we substitute various x-values into this equation and plot the resulting points on the graph.
2. Vertical Stretching:
To vertically stretch the graph of the function by a factor of 4, we adjust the dependent variable, y.
The equation for vertically stretching is:
y = kf(x),
where k represents the stretching factor.
In this case, k = 4, so the vertical stretching equation becomes:
y = 4(x^3)
To find the graph of the function after being vertically stretched by a factor of 4, we substitute various x-values into this equation and plot the resulting points on the graph.
Remember, the stretching affects both the x-values (horizontal) and the y-values (vertical). By adjusting either of these variables, we can modify the shape and size of the graph accordingly.
To understand horizontal and vertical stretching of a graph, let's start by discussing what happens when we manipulate the equation of a graph.
For the equation y = x^3, let's first consider what this graph looks like without any stretching. This graph is a basic cubic function, which is symmetric across the y-axis and passes through the origin (0,0). It generally has a steep slope as x values increase.
Now, let's move on to horizontal stretching by a factor of 4. To horizontally stretch a graph, we need to manipulate the x-values.
One way to achieve this is by manipulating the equation itself. To stretch the graph horizontally by a factor of 4, we can replace "x" with "(x/4)" in the equation. This means that for every x-value on the original graph, we divide it by 4 on the new graph.
So, for y = x^3, if we horizontally stretch it by a factor of 4, the new equation becomes y = (x/4)^3.
To graph this, we can make a table of x and y values. For example, if we choose x = 1 on the original graph, we would have y = 1^3 = 1. However, on the horizontally stretched graph, since x = 1/4, we have y = (1/4)^3 = 1/64. We can repeat this process for other values of x to plot the new graph.
Moving on to vertical stretching, this involves manipulating the y-values. To vertically stretch a graph by a factor of 4, we multiply the y-values by 4.
For the original equation y = x^3, if we vertically stretch it by a factor of 4, the new equation becomes y = 4x^3.
Again, we can create a table of x and y values to plot the new graph. To achieve this, we multiply the y-values of the original graph by 4. For example, if we choose x = 1 on the original graph, we have y = 1^3 = 1. But on the vertically stretched graph, y = 4(1^3) = 4. We repeat this process for other values of x to plot the new graph.
In summary, horizontal stretching involves modifying the x-values of the equation, while vertical stretching involves modifying the y-values. To horizontally stretch a graph by a factor of 4, replace "x" in the equation with "(x/4)". To vertically stretch a graph by a factor of 4, multiply the y-values by 4. By applying these transformations to the original equation y = x^3, you can find the graph horizontally and vertically stretched by a factor of 4.