Graphical Inverses
Algebraic Inverses
Log/Exponent Rules
Applications in the World
100
Sketch this function's inverse (line of reflection provided):
What is (in green)
100
The inverse of this function:
y=2x^2-4
What is
y=\pm sqrt{\frac{x+4}{2}}
100
Simplify using exponent rules
\frac{6c^7u^{-8}}{(-3u^{-2})^2}
What is
\frac{2c^7}{3u^4}
100
The equation that represents this situation: During COVID, rollerblade sales have tripled yearly, with an initial sale amount of $50 million.
What is
y=50000000(3)^x
y=50(3)^x
200
Sketch this function's inverse:
What is (in black)
200
The inverse of this function:
y=\frac{1}{4}log(\frac{1}{3}x+6)+7
What is
y=3(10^{4x-28}-6)
200
Condense and solve
log_2(x^2+4)-log_2(5)=2
What are 4, -4?
200
The equation that represents this situation: In 2019, about 50 million adults in the US received mental health support. In 2021, about 113 million adults in the US received mental health support.
What is
y=50(1.5)^x
300
Sketch the INVERSE of this function:
y=sqrt{x+4}-2
What is (in purple) 
300
The inverse of this function:
y=5 \ \root{12}{x+7}-8
What is
(\frac{x+8}{5})^12-7 \ if \ x\ge-8
300
Expand and solve
log(\frac{\root{3}{b^4}}{a^5c^3})
log(a)=-1, \ log(b)=12, \ log(c)=-3
What is 30?
300
The day that gas cost $3.50 per gallon based on this situation: At the beginning of February, 2021, gas cost $3.37 per gallon in California (on average). By February 28th (28 days from the initial cost), gas cost $3.67 per gallon.
What is between February 12 and 13th?