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How do you find the range and intercepts of the function f(x)=4|x+5| ?

medlockb1234  Sep 17, 2017
edited by medlockb1234  Sep 17, 2017

Best Answer 

 #1
avatar+2198 
+2

The range is the set of all possible outputs that a function can produce. 

 

\(f(x)=4|x+5|\)

 

The absolute value of any number will can result in a positive number or 0, and 4 multiplied by a positive number or 0 does not change this property at all. Therefore, the range is the following:

 

\(\text{Range}:\{\mathbb{R}|\hspace{1mm}y\geq0\}\)

 

This means that the range can be all nonnegative numbers. In interval notation, it would look like the following:

 

\(\text{Range}:[0,+\infty)\)

 

How do we find the intercepts? To do it without a graph, you can figure out by setting x=0 and y=0 and solving in each case. Let's do that.

 

\(y=4|x+5|\) Plug in 0 for x. This time, we are solving for the y-intercept.
\(y=4|0+5|\) Simplify inside the absolute value first.
\(y=4|5|\)  
\(y=4*5=20\) We have now determined the coordinates of the y-intercept.
\((0,20)\) This is the exact coordinates of the y-intercept.
   

 

Let's do the exact same process. This time, however, we set y=0 to find the x-intecept.

 

\(y=4|x+5|\) Set y equal to 0.
\(0=4|x+5|\) Divide by 4 on both sides.
\(0=|x+5|\) The absolute value always splits an equation into its plus or minus. However, 0 is neither positive nor negative, so there aren't 2 equations that one can set up.
\(x+5=0\)  
\(x=-5\) We have now determined the x-intercept, as well.
\((-5,0)\)  
   
TheXSquaredFactor  Sep 17, 2017
 #1
avatar+2198 
+2
Best Answer

The range is the set of all possible outputs that a function can produce. 

 

\(f(x)=4|x+5|\)

 

The absolute value of any number will can result in a positive number or 0, and 4 multiplied by a positive number or 0 does not change this property at all. Therefore, the range is the following:

 

\(\text{Range}:\{\mathbb{R}|\hspace{1mm}y\geq0\}\)

 

This means that the range can be all nonnegative numbers. In interval notation, it would look like the following:

 

\(\text{Range}:[0,+\infty)\)

 

How do we find the intercepts? To do it without a graph, you can figure out by setting x=0 and y=0 and solving in each case. Let's do that.

 

\(y=4|x+5|\) Plug in 0 for x. This time, we are solving for the y-intercept.
\(y=4|0+5|\) Simplify inside the absolute value first.
\(y=4|5|\)  
\(y=4*5=20\) We have now determined the coordinates of the y-intercept.
\((0,20)\) This is the exact coordinates of the y-intercept.
   

 

Let's do the exact same process. This time, however, we set y=0 to find the x-intecept.

 

\(y=4|x+5|\) Set y equal to 0.
\(0=4|x+5|\) Divide by 4 on both sides.
\(0=|x+5|\) The absolute value always splits an equation into its plus or minus. However, 0 is neither positive nor negative, so there aren't 2 equations that one can set up.
\(x+5=0\)  
\(x=-5\) We have now determined the x-intercept, as well.
\((-5,0)\)  
   
TheXSquaredFactor  Sep 17, 2017

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