Exam 1 Review Tuesday

Exponents

100

For any number, other than zero, a⁰ = ?

1

200

How do you get rid of a negative exponent?

Move it from the numerator to denominator or vice versa. 

300

3⁴*3²

3⁶

400

5⁶ / 5²

5⁴

500

(7³)⁴

7¹²

Radical and Rational Expressions

100

sqrt(81) - sqrt(6) + 4sqrt(6)

9 + 3sqrt(6)

200

sqrt(5a³b⁵) * sqrt(125ab³c⁵)

5a²b⁴c²*sqrt(c)

300

sqrt(26a⁵) / sqrt(2a²b)

a * sqrt(13a/b)

400

rationalize (5 + sqrt(3)) / (3 - sqrt(2))

(15 + 5sqrt(2) + 3sqrt(3) + sqrt(6)) / 7 

500

5th root of 36

36^1/5

Exponential Functions

100

What is the domain? range? 

domain: all real numbers

range: (0 , infinity)

200

Horizontal asymptote?

y = 0 

300

x-intercept? y-intercept?

no x-intercept

y-intercept is one

400

compound interest formula? 

y = p ( 1 + r/n)^nt

500

You start out with $3,000 in your bank account. You earn 5% interest every month. How much, to the nearest cent, do you have after 5 years?

$56,037.56

Exponential w/Transformations

100

What transformation is occurring in: 2^x-1

vertical shift down 1

200

What transformation is occurring: 2^x-3

Horizontal transformation to the right 3. 

300

What transformation is occurring: (1/5)2^x

Vertical compression by 1/5

400

What transformation is occurring here: -2​^x​​​

Reflection over the x-axis

500

What transformation is occurring here: 2^-x

Reflection over the y-axis

Inverses/Functions

100

How do you know if something is a function? 

vertical line test

200

How do you know if something is one-to-one?

Horizontal line test

300

In order to have an inverse that has no domain restrictions, what must be true about the function?

It must be one-to-one.

400

How can you check if two functions are inverses?

Composition both ways will result in x:

f(f^-1(x)) = x = f^-1(f(x))

500

Find the inverse of y = 7x - 5

y = (x+5)/7