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mihalych1998 [28]
4 years ago
6

how does subtracting a positive constant, k, from an exponential function affect its horizontal asymptote?

Mathematics
1 answer:
Setler [38]4 years ago
5 0

Answer:

horizontal asymptote shifts down k units.

Step-by-step explanation:

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Let f(x)=x^3-x-1
alexira [117]
f(x) = x^3 - x - 1

To find the gradient of the tangent, we must first differentiate the function.

f'(x) = \frac{d}{dx}(x^3 - x - 1) = 3x^2 - 1

The gradient at x = 0 is given by evaluating f'(0).

f'(0) = 3(0)^2 - 1 = -1

The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.

The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so

y = -x + c

Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).

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y = -x + c \\\\ -1 = -(0) + c \\\\ -1 = c \\\\ \text{Equation of tangent is } \boxed{y = -x - 1}
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3 years ago
How much money will be in a bank account after 4 years if $8 is deposited at an interest rate of 5%? a. $12.00 b. $10.41 c.$16.0
vichka [17]
C: 16.00 because when I multipled it was 16
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The sum of the two digit number is 12. If the digit are revesed, then the new number is 18 less than the originaol muber that is
FromTheMoon [43]

Answer:

A) X + Y = 12

B) 10Y + x = 10x + Y -18

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Double-Check

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Step-by-step explanation:


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The second blank is AL

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The fourth and final blank is GH

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 product is multiplication:

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3 years ago
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