f(x) = tan(x) Interesting fact: The tangent function is a ratio of the sine and cosine functions. f(x) = Directions: Cut out the 15 parent function cards. Label each graph by its equation and by its name from the lists below. The Absolute Value Function The Cosine Function The Cubing Function The Exponential Function The Greatest Integer Function The Identity Function The Inverse-Square Function The Logarithmic Function The Natural Exponential Function The Natural Logarithmic Function The Reciprocal Function The Sine Function The Square Root Function The Squaring Function The Tangent Function Interesting fact: The origin is called a “point of inflection” for this curve because it changes curvature at that point xx Interesting fact: The extrema of this function occur at the zeros of the sine function.

Domain is   n , (where n is an integer) Range is . It is odd. y-intercept (0,0). x-intercepts (n ,0), (where n is an integer) Vertical asymptotes at x=  n , (where n is an integer) It increases on each interval of the domain. It is not bounded above or below. It has no extrema. It oscillates between -  and . Asymptotes Boundedness Domain End Behavior Extrema Increasing/decreasing behavior Range Symmetry x- & y-intercepts Directions: On the back of each card list the properties of the parent function. You’ll have to do some research and investigation to find out all to the info so include a list of sources, textbooks, websites etc where you found the information.

(b,1) 1b (e,1) (1, e) Interesting fact: This function has a ”sharp turn” while the other parent functions are “smooth” for their domains f(x) = Interesting fact: The number e is an irrational number (like  ). Interesting fact: This function, along with trigonometric and exponential, is called a transcendental function. b - (1, b) 1 - Interesting fact: This function, along with trigonometric and exponential, is called a transcendental function. Interesting fact: This function, along with trigonometric and logarithmic, is called a transcendental function. Interesting fact: This function can we rewritten with a fractional exponent

Interesting fact: This graph is called an hyperbola and this function is a rational function Interesting fact: This graph is called a parabola and this function is a quadratic function. Interesting fact: This function is also called the Floor Function and can also be written as f(x) =[|x|] f(x) = Interesting fact: The extrema of this function occur at the zeros of the cosine function. Interesting fact: This is a polynomial function with a degree of one Interesting fact: This function, (like the Rational Function) can be rewritten with a negative exponent.