Answer:
the function is continuous from the left at x=1 and continuous from the right at x=0
Step-by-step explanation:
a function is continuous from the right , when
when x→a⁺ lim f(x)=f(a)
and from the left when
when x→a⁻ lim f(x)=f(a)
then since the functions presented are continuous , we have to look for discontinuities only when the functions change
for x=0
when x→0⁺ lim f(x)=lim e^x = e^0 = 1
when x→0⁻ lim f(x)=lim (x+4) = (0+4) = 4
then since f(0) = e^0=1 , the function is continuous from the right at x=0
for x=1
when x→1⁺ lim f(x)=lim (8-x) = (8-0) = 8
when x→1⁻ lim f(x)=lim e^x = e^1 = e
then since f(1) = e^1=e , the function is continuous from the left at x=1
Answer:
Equation = y = -4x+7
See the graph below
Step-by-step explanation:
The equation of the line in slope intercept form is expressed as;
y = mx+c
Given
slope m = -4
y-intercept c = 7
Substitute
y = -4x + 7
Get the x intercept.
at y = 0
0 = -4x + 7
4x = 7
x = 7/4
x = 1.75
The x coordinate (1.75, 0)
Get the y intercept
at x = 0;
y = -4(0)+7
y = 0+7
y = 7
The y coordinate is (0, 7)
Yes but it dose depend on the problem
