What is the graph of the function rule? Y=|5x|-2
You surely know that the graph of y=|x| is a V shape with the point of the V at (0,0)
So, what do you have to do to it to get to your rule?
So, what's the answer?
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Oh, the graph of this function is quite the showstopper! It's like a roller coaster ride with a twist. Imagine a regular ol' graph, but then give it a little attitude. The graph starts at the origin (0, 0) and shoots off in two different directions.
On one side, it hugs the positive x-axis like it's searching for a lost coin in a couch. But it's a bit overdramatic, so it overcompensates and shoots up like a rocket ship. That's the positive part of the graph.
On the other side, it cuddles up to the negative x-axis, almost as if it's looking for a shoulder to cry on. But then, with a graceful motion, it flips upside down, like a gymnast nailing a triple somersault. That's the negative part of the graph.
And what about that absolute value part? It's like a referee trying to keep things fair. It swoops in and says, "Hey, no negativity here!" It snatches up any negative values and turns them into positive ones.
So there you have it! A graph that's bold, dramatic, and always positive. Just like a clown performing the grandest act at the circus!
To understand the graph of the function rule y = |5x| - 2, we'll follow a step-by-step process:
Step 1: Understand the Absolute Value Function
The function y = |x| represents the absolute value of x, which means it returns the distance between x and 0 on the number line. For positive values of x, |x| = x, and for negative values of x, |x| = -x. The absolute value function always returns a non-negative value.
Step 2: Transform the Absolute Value Function
In this case, the absolute value function is multiplied by 5 and then subtracted by 2. Let's break it down:
- Multiplying by 5 vertically stretches the graph, making it thinner vertically.
- Subtracting 2 shifts the entire graph downward by 2 units.
Step 3: Sketch the Graph
To sketch the graph, we start with the graph of the absolute value function y = |x| (a "V" shape) and make the necessary transformations.
- To apply the vertical stretch, we need to divide the x-coordinates by 5 (since it's multiplied by 5 in the function rule). This will make the graph wider horizontally.
- Then, we subtract 2 from the y-values of the original graph to shift it downward.
After applying these transformations, we have the graph of the function y = |5x| - 2, which is wider horizontally, shifted downward by 2 units compared to the original y = |x| graph.
Note that the graph will only exist in the portion where the input x is defined. If there are no restrictions on x, the graph will extend indefinitely in both the positive and negative x-directions.
y = | 5 x | - 2 mean:
y = ± 5 x - 2
1.
y = 5 x - 2
2.
y = - 5 x - 2
These are two straight lines.
Find x and y intercepts for both.
x- intercept is a point on the graph where y is zero
y- intercept is a point on the graph where x is zero
1.
y = 5 x - 2
x- intercept
5 x - 2 = 0
add 2 to both sides
5 x - 2 + 2 = 0 + 2
5 x = 2
Divide both sides by 5
x = 2 / 5
x- intercept:
x = 2 / 5 , y = 0
x = 0.4 , y = 0
You can write this like x- intercept ( 0.4 , 0 )
y- intercept
y = 5 ∙ 0 - 2
y = 0 - 2
y = - 2
y- intercept:
x = 0 , y = - 2
You can write this like y- intercept ( 0 , - 2 )
Draw straight line which connects point ( x = 0.4 , y = 0 )
and point x = 0 , y = - 2
2.
y = - 5 x - 2
x- intercept
- 5 x - 2 = 0
add 2 to both sides
- 5 x - 2 + 2 = 0 + 2
- 5 x = 2
Divide both sides by - 5
x = - 2 / 5
x- intercept:
x = - 2 / 5 , y = 0
x = - 0.4 , y = 0
You can write this like x- intercept ( - 0.4 , 0 )
y- intercept
y = - 5 x - 2
y = ( - 5 ) ∙ 0 - 2
y = 0 - 2
y = - 2
y- intercept:
x = 0 , y = - 2
You can write this like y- intercept ( 0 , - 2 )
Draw straight line which connects point ( x = - 0.4 , y = 0 )
and point x = 0 , y = - 2
If you want to see the graph go on:
wolframalpha.c o m
When page be open in rectangle type:
plot y = | 5 x | - 2 , x = - 1 to 1
and click option =
You will see the graph.