2) For the graphs f and g given : c) Find the values of x for which g( x) f ( x)

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1 Algebra Per Name Concept Category 1 - Functions Teacher: N Student: N ) Domain : Range : End Behavior Interval of increase : f (3) f (4) decrease : f ( x) 1 x? x intercept y intercept ) For the graphs f and g given : a) Find the values of x for which g( x) f ( x) b) Find the values of x for which g( x) f ( x) c) Find the values of x for which g( x) f ( x) 3) Sketch : ( x 5) x 3 f ( x) x 1 3 x 3 3 x x Evaluate : f(3) f( 3)

2 4) a) Create a piecewise equation for the graph : b) What do you have to modify on the graph to make it continuous? Create a new equation for the modified graph c) What do you have to modify on that the graph so the graph contains point(7, 0)? Create a new equation for the modified graph

3 Algebra Name: Per.: Date: Concept Category : Exponential Functions and Logarithms Mastery: NY DOK 1] 1. Solve: x Convert 1 to rational exponent. Find the x with the given logarithms. a.) log x 5 b.) log 1 x 3 3 DOK ] 3. Solve each logarithmic equation. a.) log (3x ) 3log 4 b.) log3 4 log 3( x 4) log Sketch the functions: f x f ( x) 3log ( x ) 4 ( x 3) ( ) 3 4 At least one coordinate: At least one coordinate: Y-Intercept for the final graph: X-Intercept for the final graph: Horizontal Asymptote for the final graph: Vertical Asymptote for the final graph:

4 DOK 3] 5. The half-life of a medication is the amount of time for half of the drug to be eliminated from the body. The half-life of Advil or ibuprofen is hours: a) Create an equation. b) A 340 milligram dosage of Advil is taken at 7:30 pm. How many milligrams of the medication will remain in the body at 1:00 am? b) How many hours will it take for 40 milligram dosage of Advil in a person s body to equal 10 milligrams? 6. The bacteria E. coli often cause illness among people who eat infected food. Suppose that 400 E. coli bacterium are planted in a batch of ground beef and begins doubling every minute. a) Write an equation that can be used to calculate the number of bacteria in the food after any number of minutes. Let x = # of minutes. y = # of bacteria. b) How many bacteria will there be after 5 minutes have elapsed? (Assume no bacteria die.) c) How long does it take for the bacteria population to reach 68384?

5 Name: Period: Date: //18 Concept Category 3 Concept Category 4 Recall & Reproduction Quadratic Equations Polynomial Equations Teacher: NY i 1. Multiply i 4 3i. Multiply Rationalize 3 i 3. For each given graph, create an equation : Routine 4. Given g( x) 3( x 4) 6 5. Given g( x) x 4x 3 a] Find the vertex po int a] Find the vertex po int b] Find the roots b] Find the roots 6. Given g( x) 8x 6x 0 a] Find the vertex point b] Find the roots by factoring

6 CC DOK Sketch g x x 3 4 ] ( ) 0.0(x 1) ( 8x 16)(x 5x 6) 8) Solve x x x x : 8 ( 4) 8 9) Create an equation with roots 1 1,,,3 and y intercept 8 10) Is ( x 3) a factor of 3 f ( x) x 3x 3x 15? If it is a factor, write f(x) in a factored form. Non-Routine 10) CC3] A projectile is fired from a cliff 00 feet above the water at an inclination of 45 to the horizontal, with a muzzle velocity of 50 feet per second. The height h of the projectile above the water is given by 8x h( x) x 300 where x is the horizontal distance of the projectile from the face of the cliff. 5 a) At what horizontal distance from the face of the cliff is the height of the projectile a maximum? b) At what horizontal distance from the face of the cliff will the projectile strike the water? c) When the height of the projectile is 100 feet above the water, how far is it from the cliff? 11) CC4 Find an equation of the polynomial function with 3 distinct roots and rational coefficients with degree 7 that goes through (0, 8). It bounces at 1 and twitch (flattens) through - and has the factor (x-3). Write the equation in factored form and explain how you found each factor. 1) CC4 Sketch 4 3 f ( x) 3x 16x 1x 4x 1 if ( x 3x ) are two of the factors for f( x ) 13) CC3 The shaded area = 140 cm square, solve for x

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