### About Function Notation:

When we work with functions, we have a specific notation that applies. Generally, instead of y, we will now see f(x), g(x), or h(x). When we have a function, we can use the notation to ask for the function's value, given a certain input. If we see f(2), this means replace the independent variable with 2 and evaluate.

Test Objectives

- Demonstrate the ability to write a function using function notation
- Demonstrate an understanding of f(a), where a is a real number
- Demonstrate an understanding of f(x + a), where a is a real number

#1:

Instructions: Find f(0), f(-1), and f(-5).

a) $$f(x)=7x^2 - x + 5$$

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#2:

Instructions: Find f(-2), f(6), and f(12).

a) $$f(x)=-\frac{1}{4}x + 3$$

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#3:

Instructions: Find f(c), f(c + 3), and f(c - 1).

a) $$f(x)=-x^2 + 5x - 9$$

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#4:

Instructions: Find f(-2), and f(z-3).

a) $$-9x + 3y=-24$$

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#5:

Instructions: Find f(-3), and f(b + 4)

a) $$2x^2 + 4y=-12$$

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Written Solutions:

#1:

Solutions:

a) $$f(0)=5$$ $$f(-1)=13$$ $$f(-5)=185$$

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#2:

Solutions:

a) $$f(-2)=\frac{7}{2}$$ $$f(6)=\frac{3}{2}$$ $$f(12)=0$$

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#3:

Solutions:

a) $$f(c)=-c^2 + 5c - 9$$ $$f(c + 3)=-c^2 - c - 3$$ $$f(c - 1)=-c^2 + 7c - 15$$

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#4:

Solutions:

a) $$f(-2)=-14$$ $$f(z-3)=3z - 17$$

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#5:

Solutions:

a) $$f(-3)=-\frac{15}{2}$$ $$f(b + 4)=-\frac{b^2}{2}- 4b - 11$$