QUADRATIC. Parent Graph: How to Tell it's a Quadratic: Helpful Hints for Calculator Usage: Domain of Parent Graph:, Range of Parent Graph: 0,

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1 Parent Graph: How to Tell it's a Quadratic: If the equation's largest exponent is 2 If the graph is a parabola ("U"-Shaped) Opening up or down. QUADRATIC f x = x 2 Domain of Parent Graph:, Range of Parent Graph: 0, *For ANY quadratic function, the domain will be the same, and the range will always have one resrticted side just depending on where the lowest (if it opens up) or highest (if it opens down) point on the graph is* Helpful Hints for Calculator Usage: The "x 2 " button will give you the squared. Be careful when entering equations and be sure to use parenthesis!! Example: y = 2 x You need to be sure that you include the parenthesis and then put the squared on the outside.

2 Parent Function Graph: How to Tell it's a Linear: If the equation has no exponents larger than 1 If the graph is a straight line. LINEAR f x = x Domain of Parent Function:, Range of Parent Function:, *This will be the same domain and range for ALL linear functions* Helpful Hints for Calculator Usage: Be sure that if you are typing in a negative as the first part of the equation that you use the negative sign and not the subtraction sign.

3 Parent Function Graph: How to Tell if it's an Absolute Value: If the equation has the absolute value bars. If the graph has a "V" Shape, opening up or down. Absolute Value f x = x Domain of Parent Function:, Range of Parent Function: 0, *For ANY absolute value function, the domain will be the same, and the range will always have one resrticted side just depending on where the lowest (if it opens up) or highest (if it opens down) point on the graph is* To get the Absolute Value bars in your calculator: Math Num abs( Be sure to close the parenthesis when the absolute value bars end. Example: y = 3 x would look like 3abs x in the calculator.

4 Parent Function Graph: How to Tell if it's a Square Root: If the equation has the square root symbol. If the graph has only one arrow and has a slight curved shape. SQUARE ROOT f x = x Domain of Parent Function: 0, Range of Parent Function: 0, *The Domain and Range of ANY square root function will always have one restricted side (depending on where the graph starts) and one infinity side (depending on the direction of the arrow)* To get the Square Root symbol on your calculator: 2 nd x 2 Be sure to close the parenthesis when the square root symbol ends. Example: y = 3 x would look like 3 x in the calculator.

5 Parent Function Graph for 0<b<1: Parent Function Graph for b>1: How to Tell if it's an Exponential: If the equation has the x-variable in the exponent. The graph has a HORIZONTAL boundary where the graph gets very close to, but NEVER touches or crosses. Asymptote: y = 0 Domain of Parent Function:, Use the carrot key "^" to denote the Range of Parent function: 0, start of the exponent, and then put everything that is in the exponent in ( ). *The Domain of ANY exponential function will be the same, the range will vary based on where the asymptote is and what side of the asymptote the graph is on. The restricted side will always have a "(" not a "["* EXPONENTIAL f x = b x (b is any positive number) Example: y = 3 x+2 1 will look like 3^(x+2) - 1 in the calculator REMEMBER: VERTICAL translations move asymptote

6 Parent Function Graph for 0<b<1 Parent Function Graph for b>0 Domain of Parent Function: 0, Range of Parent function:, *The Range of ANY logarithmic function will be the same, the domain will vary based on where the asymptote is and what side of the asymptote the graph is on. The restricted side will always have a "(" not a "["* LOGARITHMIC f x = log b (x) (b is any positive number) Asymptote: x = 0 How to Tell if it's a Logarithmic: If the equation has "log" or "ln" in it. If the graph has a VERTICAL boundary where the graph gets very close to, but NEVER touches or crosses. We have to use change of base formula to be able to plug most log functions into calculator: log b (x) = log(x) log(b) Example: y = log 7 x + 1 will look like (log(x + 1)/ log(7)) in the calculator REMEMBER: HORIZONTAL translations move asymptote