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Section 1

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Starting with the graph of y = e^x, write the equation of the graph that shrinks horizontally by a factor of a.

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Mar 1, 2020

Cards (35)

Section 1

(35 cards)

Starting with the graph of y = e^x, write the equation of the graph that shrinks horizontally by a factor of a.

Front

y=e^ax

Back

Find the values of x where the function f(x) is discontinuous.

Front

Take the limit as x -> the number from the left and right equations. x − 3 if x ≤ −3 x^2 + 6x + 3 if −3 < x ≤ 1 lim x -> -3 from the left (-3) - 3 = -6 lim x -> -3 from right (-3)^2+6(-3)+3= -6 so the function is continuous at -3.

Back

Definition of Derivative

Front

lim h->0 (f(x+h)-f(x))/h

Back

Exponential Function

Front

f(x) = b^x (where b is a positive constant)

Back

Derivative of Sec(x)

Front

tan(x)sec(x)

Back

Derivative of sin^-1 (x)

Front

1/sqrt 1-x^2

Back

ln(e) =

Front

1

Back

sin(2x)

Front

2SinxCosx

Back

Find the limit of a function containing a trigonometric function.

Front

Squeeze theorem

Back

Starting with the graph of y = e^x, write the equation of the graph that results reflecting about the y-axis

Front

y=e^-x

Back

The laws of exponents

Front

1) b^x*b^y = b^x+y 2) b^x/b^y = b^x-y 3) (b^x)^y = b^xy 4) (ab)^x = a^x⁢b^x 5) b^-x = 1/b^x 6) b^(1/n) = nSqrtb

Back

how to find vertical asymptote at x = 5

Front

Vertical asymptote is when the limit approaches infinity or negative infinity from the right or the left. Take the limit as x -> 5, simplify first if denominator goes to zero and plug 5 in for x.

Back

Intermediate Value Theorem (IVT)

Front

If f is continuous on the closed interval [a,b] and n is any number between f(a) and f(b), then there exists some number c between [a,b] such that f(c)=n

Back

To find the limit of a function with a square root

Front

conjugate

Back

Find vertical asymptotes of f(x)

Front

Find when the denominator = 0; Express f(x) as a fraction, express numerator and denominator in factored form, and do any cancellations. Set denominator equal to 0.

Back

Starting with the graph of y = e^x, write the equation of the graph that results shifting 2 units downward.

Front

y=e^(x) -2

Back

Find horizontal asymptotes of f(x)

Front

Find limit as x approaches infinity of f(x) and limit as x approaches negative infinity of f(x)

Back

cos(2x)=2cos^2(x)-1

Front

Back

Derivative of Csc(x)

Front

-cot(x)csc(x)

Back

Derivative of Tan(x)

Front

sec^2(x)

Back

Starting with the graph of y = e^x, write the equation of the graph that results shifting 1 units to the right.

Front

y=e^(x-1)

Back

Show that the equation has at least one real solution/root

Front

Intermediate Value Theorem

Back

Starting with the graph of y = e^x, write the equation of the graph that stretches horizontally by a factor of a.

Front

y=e^(x/a)

Back

To find domain of a square root (x)

Front

find when x > 0;

Back

Starting with the graph of y = e^x, write the equation of the graph that shrinks vertically by a factor of a.

Front

y=1/a e^x

Back

ln(1) =

Front

0

Back

Derivative of Sin(x)

Front

cos(x)

Back

Find horizontal asymptotes of f(x)

Front

Find limit as x approaches infinity of f(x) and limit as x approaches negative infinity of f(x)

Back

What is the letter e?

Front

e is the precise base number of function exponential function f(x) = b^x, so that the tangent line at (0,1) = 1. The tangent line for the graph of f(x)=e^x at point (0,1) will be 1.

Back

Starting with the graph of y = e^x, write the equation of the graph that results reflecting about the x-axis

Front

y= -e^x

Back

Derivative of Cot(x)

Front

-csc^2(x)

Back

Sin^2 (x) + Cos^2 (x) =

Front

1

Back

Derivative of Cos(x)

Front

-sin(x)

Back

When is ln(x) defined?

Front

x > 0

Back

Starting with the graph of y = e^x, write the equation of the graph that stretches vertically by a factor of a.

Front

y=ae^x

Back