# Function notation #### All in One Place

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##### Intros
###### Lessons
1. Introduction to function notations
Equations VS. Functions
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##### Examples
###### Lessons
1. If $f(x) = 5x^2-x+6$ find the following
1. ${f(\heartsuit)}$
2. ${f(\theta)}$
3. ${f(3)}$
4. ${f(-1)}$
5. ${f(3x)}$
6. ${f(-x)}$
7. ${f(3x-4)}$
8. ${3f(x)}$
9. ${f(x)-3}$
2. If f(x) = 6 - 4x, find:
1. f(3)
2. f(-8)
3. f(-2/5)
3. If f(r) = $2\pi r^2h$, find f(x+2)
1. If ${f(x) = \sqrt{x},}$ write the following in terms of the function ${f.}$
1. ${\sqrt{x}+5}$
2. ${\sqrt{x+5}}$
3. ${\sqrt{2x-3}}$
4. ${-8\sqrt{x}}$
5. ${-8\sqrt{2x-3}}$
6. $4\sqrt{x^{5}+9}-1$
2. If f(x) = -3x + 7, solve for x if f(x) = -15
1. The temperature below the crust of the Earth is given by C(d) = 12d + 30, where C is in Celsius and d is in km.
i.) Find the temperature 15 km below the crust of the Earth.
ii.) What depth has a temperature of $186^\circ$C?
###### Topic Notes
Function notation is another way to express the y value of a function. Therefore, when graphing, we can always label the y-axis as f(x) too. It might look confusing, but let us show you how to deal with it.