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# Module 3 Study Stack

### Function notation and Graphing

Question | Answer |
---|---|

Find the equation that goes through the points (3,-8) and (5,12). Write in function notation. | Slope (M) = 10 Function notation (using point (5,12)): f(x)=10x-115 |

What is function notation? | Function notation is the "x" value of a point. When written as "f(3)=10", the corresponding point is (3,10). |

What is the difference between (1) -squareroot of a, (2) squareroot of a, and (3) squareroot of -a? | (1) The answer for these types of square roots are -a. (2) The answer for these types of square roots is a. (3) The answer for these types of square roots are NOT real numbers. |

Solve for the following: (1) -Squareroot of 36 (2) Squareroot of -121 (3) Squareroot of 169 | (1) -6 (2) Not a real number (3) 13 |

What is a nonlinear function? | Nonlinear functions are: f(x)=x^2 (squared) f(x)=IxI (absolute value) f(x)=squareroot of x |

Describe the graph: (1) f(x)=x^2 (2) f(x)=IxI (3) f(x)= squareroot of x | (1) Parabola (2) V-shaped (3) Curved to the right |

How do you move a graph vertically? | y=mx+b -> the "b" moves the graph up and down. +b moves up, -b moves down. g(x)=f(x)+k -> same concept as "b" |

How do you move a graph horizontally? | g(x)=f(x+h)^2 ; g(x)=f(x-h)^2 -> "h" moves a graph left or right. When +h, that means to move LEFT and when -h, that means to move the graph RIGHT |

What does it mean to be "reflected"? | Reflection means that a graph is flipped upside down, or, negative. |

How do I know if a graph is reflected? | The equation for a reflected graph will have a negative (-) sign in front of it. Example: f(x)=-IxI; this reflects the absolute value graph (V-shaped) downward. |

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