Answer:
Range is y > 0
Step-by-step explanation:
We need to find the range of y = e^4x
The range is defined as a set of values of dependent variable for which the function is defined.
The exponential function of form c. n^x + k has range f(x) > k
in the given function y = e^4x ,k =0
so Range is y > 0
Answer:
7
Step-by-step explanation:
4
can be written as ![\frac{14}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B14%7D%7B3%7D)
number of
portions =
÷ ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
=
x ![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D)
=
= 7
Answer:
[See Below]
Step-by-step explanation:
<h2>For Point Slope Form:</h2>
Point slope form is: ![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
'm' is the slope
(x1, y1) is a coordinate point.
<h3>Slope:</h3>
Slope is rise over run. ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We are given the points (-1,5) and (3,-3).
![\frac{-3-5}{3-(-1)}=\frac{-8}{4}= -2](https://tex.z-dn.net/?f=%5Cfrac%7B-3-5%7D%7B3-%28-1%29%7D%3D%5Cfrac%7B-8%7D%7B4%7D%3D%20-2)
The slope of the line is -2.
I will use (-1,5) as the point:
![y-y_1=m(x-x_1)\rightarrow\boxed{y-5=-2(x+1)}](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29%5Crightarrow%5Cboxed%7By-5%3D-2%28x%2B1%29%7D)
<h2>For Slope Intercept:</h2>
Slope intercept is: ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
'm' - Slope
'b' - y-intercept
We can use the point slope equation to convert it into slope intercept form:
![y-5=-2(x+1)\\\\y-5=-2x-2\\\\y-5+5=-2x-2+5\\\\\boxed{y=-2x+3}](https://tex.z-dn.net/?f=y-5%3D-2%28x%2B1%29%5C%5C%5C%5Cy-5%3D-2x-2%5C%5C%5C%5Cy-5%2B5%3D-2x-2%2B5%5C%5C%5C%5C%5Cboxed%7By%3D-2x%2B3%7D)
<h2>For Standard Form:</h2>
Standard form is ![Ax+By=C](https://tex.z-dn.net/?f=Ax%2BBy%3DC)
Using out slope intercept form equation:
![y=-2x+3\\\\y+2x=-2x+2x+3\\\\1y+2x=3\\\\\boxed{2x+1y=3}](https://tex.z-dn.net/?f=y%3D-2x%2B3%5C%5C%5C%5Cy%2B2x%3D-2x%2B2x%2B3%5C%5C%5C%5C1y%2B2x%3D3%5C%5C%5C%5C%5Cboxed%7B2x%2B1y%3D3%7D)
Answer:
{x : x ε Z where x<3 & x>4}