College Algebra Exam 2

College Algebra Exam 2 ( 2.4—3.2) Name: ______________________________________ Q1. (10 points) Given 𝑓(π‘₯) = 4 βˆ’ 2π‘₯; A) Determine whether the given function is linear. If the function is linear, express the function in the form 𝑓(π‘₯) = π‘Žπ‘₯ + 𝑏. B) Find the slope of the function. C) Determine the net change between π‘₯ = 1 π‘Žπ‘›π‘‘ π‘₯ = 3 D) Determine the average rate of change between π‘₯ = 1 π‘Žπ‘›π‘‘ π‘₯ = 3 Q2. (15 points) Let 𝑓(π‘₯) = π‘₯ 2 βˆ’ 1, 𝑔(π‘₯) = 3π‘₯ + 5, find the following: a) 𝑓 βˆ’ 𝑔 b) 𝑓 βˆ™ 𝑔 𝑐) 𝑔(𝑓(2)) 1 𝑑) π‘“π‘œπ‘” College Algebra Exam 2 ( 2.4—3.2) Name: ______________________________________ Q3. A) (5 points) Graph 𝑓(π‘₯) = |π‘₯| B) (10 points) Sketch 𝑔(π‘₯) = |π‘₯ βˆ’ 5| + 2 using transformation, find its domain and range. Graph of 𝑓(π‘₯) = |π‘₯| by complete the table first. Graph of 𝑓(π‘₯) = |π‘₯| π‘₯ 𝑓(π‘₯) = |π‘₯| 2 1 0 βˆ’1 βˆ’2 Graph of 𝑔(π‘₯) = |π‘₯ βˆ’ 5| + 2 using transformation of 𝑓(π‘₯). Domain of 𝑔(π‘₯): Range of 𝑔(π‘₯): 2 College Algebra Exam 2 ( 2.4—3.2) Name: ______________________________________ Q4. (20 points) A) Given 𝑓(π‘₯) = √π‘₯ + 2, find its domain and range B) find the inverse function 𝑓 βˆ’1 , find its domain and range C) Sketch the graphs of 𝑓 and 𝑓 βˆ’1 on the same coordinate axes. 3 College Algebra Exam 2 ( 2.4—3.2) Name: ______________________________________ Q5. (15 points) For the given polynomial function 𝑔(π‘₯) = (π‘₯ βˆ’ 1)2 (π‘₯ + 2) a) Complete the table. b) List each real zero and its multiplicity c) Determine whether the graph crosses or touches the x-axis at each x-intercept d) Graph 𝑔(π‘₯) Graph of 𝑔(π‘₯) Complete the table: π‘₯ 𝑔(π‘₯) = (π‘₯ βˆ’ 1)2 (π‘₯ + 2) βˆ’3 βˆ’2 βˆ’1 0 1 2 4 College Algebra Exam 2 ( 2.4—3.2) Name: ______________________________________ Q6. (25 points) For the given function. a) Find the vertex, x-intercepts, and y-intercept b) Write it in standard form 𝑓(π‘₯) = π‘Ž(π‘₯ βˆ’ β„Ž)2 + π‘˜ c) Graph it and use its graph to find its domain and range d) Use the graph to determine where the function is increasing and where it is decreasing. e) find the maximum or minimum value 𝑓(π‘₯) = βˆ’π‘₯ 2 + 6π‘₯ + 4 5
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