Pre-Calc Unit 1 Review Jeopardy

Function Basics Special functions Function operations Transformations of functions$100 Which set represents a function?

(a) {( v ,−1 ) , (u ,2 ) , (w ,0 ) , (u ,−2 ) }(b) {(u ,−2 ) , ( v ,2 ) , (w ,1 ) }(c) {(u ,2 ) , (v ,2 ) , (w ,1 ) , (w ,1 ) }(d) {(w ,−2 ) , (v ,0 ) , (w ,2 ) }

Answer (b)

$100Evaluate the following piecewise function at h(−1)

h ( x )={2x+1 , x≤−1x2+2 , x>−1Answer: −1

$100Let f ( x )=3−2 x and let g ( x )=3 x2+2. Find ( fh) (1 )

Answer: 5

$100Take the function

f ( x )=¿x2−2∨¿ and shift it up 5 units. What’s the equation for the new function?Answer: f ( x )=|x2−2|+5

$200 Evaluate the function as indicated and simplify as much as possible:

f ( x )= x2 x−5

find f ( 5 x2x−1 )

Answer: x

$200Algebraically determine if the function is even, odd or neither

f ( x )=2x3−x2Answer: neither

$200Let f ( x )=3−2 x and

let g ( x )=(3 x2+2) find f (g ( x ) )

Answer: 3−2 (3 x2+2 )=¿3−6 x2−4=¿

−1−6x2

$200Determine how the function

f ( x )=x2 was transformed to

become g ( x )=−12

( x−3 )2+6

Answer: Was shifted right 3 units, was compressed by a factor of 2, reflected over the x axis then moved up 6 units.

$300Find the domain and range

f ( x )=√2 x2−1Answer: Domain [√22 ,∞) Range

[0 ,∞ )

$300Algebraically determine if the function is even, odd or neither

f ( x )=−(x2−8 )2Answer: Even

$300Determine if f (x) and g(x ) are inverses algebraicallyf ( x )=√x+1 , g ( x )=x2−1

Answer: yes

$300Take the function

f ( x )=¿x2−2∨¿ and shift it left 2 units. Then reflect it over the y-axis. What’s the equation for the new function?Answer: g ( x )=¿ x2−4 x+2∨¿

$400Evaluate the function as indicated and simplify as much as possible:

f ( x )=2x2+3 x−1 , f ( x+h )−f ( x )h

Answer: 4 x+3+2h

$400Algebraically determine if the function is one-to-one and explain your reasoning.

f ( x )= (x−1 )2

$400Find the inverse function for f (x) algebraically.

f ( x )=4 x3−3

Answer: 3√ x+34

$400True or False: If the graph of the common function f ( x )=x2 is moved six units to the right, moved three units upward, and reflected in the x-axis, then the point (-1,28) will lie on the graph of the transformation

Answer: False