Pre-Cal Review 13.2 Parent Functions and Their Domain

Transcription

1 Pre-Cal Review. Parent Functions and Their Domain Name: Date: Per: Parent functions are used to identif available domain and ranges. If ou can quickl think of what the function looks like, ou can quickl identif it s appropriate domain and range. It becomes easier in addition to have composite functions if ou are familiar with parent functions. = Name: What mini-picture can ou think to remember this function? = Name: What mini-picture can ou think to remember this function?

2 ln = Name: What mini-picture can ou think to remember this function? = e Name: What mini-picture can ou think to remember this function? = Name: What mini-picture can ou think to remember this function?

3 The recommendation for parent functions is to be able to draw a mini-picture for each parent function. If ou can do this, ou can quickl recall the domain and range. Let s practice: Square Root: Cubic: Cube Root: Eponential : Rational: Natural Log: sin(): cos(): Transformations: You should be familiar with up, down, left and right transformations. In addition, we have also learned reflections over the -ais. Something that is not talked about as often is reflections over the -ais. Consider the eponential function: Parent: Reflect over -ais: Reflect over -ais: = e Eamples: ) Use a complete sentence to describe how the domain changes in the Eponential Parent Function if it has been reflected over the -ais. How does this change the domain?

4 Pre-Cal Review. Homework Name: Parent Functions and Their Domain Date: Per:. Which of the following represents the domain of the parent eponential function? i) ( 0, ) j) 0, ) k) (, ) l) (,0). Which parent function is shown? m) Eponential n) Natural Log o) Quadratic p) None. Which pair represents inverse functions? m) Quadratic and Absolute value n) Rational and Linear o) Eponential and Natural Log q) Quadratic and Cubic Root. Parent Function square root functions have what domain? w) 0, ) ) ( 0, ) ) (, ) z) none. Rational functions have a domain that skips a value. What creates this union? k) The numerator roots l) The denominator roots m) It is an inverse function n) Rational functions do not have a union domain.. Which one of the following does not share the same domain for it s parent function? c) Eponential d) Quadratic e) Natual Log f) Absolute Value

5 . True/False: Parent Functions of cos() starts at the origin. c) True d) False. Which parent function(s) has a domain that is the eact same as it s range? I. Absolute Value II. Cubic III. Square Root IV. Eponential e) I and II f) I and III g) II and III h) II and IV. Consider the parent function of Natural Log. As, e) f) g) 0 0. True/False The parent eponential function can have an output value of zero h) True i) False. If the parent log function is reflected over the -ais, which would change? s) It s domain t) It s Range u) Both Domain and Range v) Nothing. True/False: Reflections are both caused b negative sign. The reflection over the -ais is when the function is negative, and the reflection over the -ais is when onl is negative. p) True q) False. The parent sin() function is transformed to sin(-). Which reflection is this? o) Reflection over the -ais p) Reflection over the -ais q) Reflection over the = line r) No change

6 . Match the function: v) w) ) e e e. Which functions resides onl in Quadrant I? b) Quadratic c) Natural Log d) Eponential e) Square Root. Match the function below. p) q) r) = = = s) None of the above 0