A discontinuity is a point that cannot exist because the x-coordinate would cause a problem in the equation. If you have a polynomial in the denominator, you must find which values of x would cause the polynomial in the denominator to evaluate to zero. Since division by zero is undefined, that would cause a discontinuity.
Let's look at your function.
is in the numerator. It is defined for every value of x. There is no problem there.
is in the denominator. This is a function defined for every value of x, but since it is in the denominator, we must exclude the x-value that would cause this polynomial to evaluate to zero.
We set it equal to zero and solve the equation for x.
For x = 0, the denominator has a value of zero, so at this point there is a discontinuity in function f(x).
The answer is:
Answer: A and C
Step-by-step explanation:
Answer:
Step-by-step explanation:
We can create a function based on this scenario.
We know that you start with $70. This would be a constant. So, we already know that our function will contain +70.
If we earn $50 a week, we know that we can create an expression here to find how much we make based on how many weeks we spend, assuming t represents the amount of weeks we spent.
We can add this to our original constant of 70.
Since the output will be a function based on how many weeks we spend, we can make it equal to s(t).
The slope here is 50, meaning that every week we earn 50 dollars more.
This means the amount of money changes by 50$ per week.
Hope this helped!
Answer:
Each dimension increased by 3 ft.
Step-by-step explanation:
Area of the original rectangle = 4 * 6 = 24 square feet
Increased dimension = x ft
New length = 6 + x
New width = 4 +x
New area = (6 + x)(4 +x) {Use FOIL method}
= 6*4 + 6*x + x*4 + x*x
= 24 + 6x + 4x + x²
= x² + 10x + 24
New area = 24 + 39
x² + 10x + 24 = 63
x² +10x + 24 - 63 = 0
x² + 10x - 39 = 0
x² + 13x - 3x - 3*13 = 0
x (x + 13) - 3(x + 13) = 0
(x + 13)(x -3) = 0 {Ignore x + 13, as it gives negative value}
x - 3 = 0
x = 3
1 chip is $10
So, for 79 chips,
= 79 x $10
= $790