+0

# Range and intercepts of a function- calculus

0
62
1
+32

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

#1
+1214
+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
Sort:

#1
+1214
+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

### 8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details