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Unit 1, Pre-test Functions Advanced Mathematics Pre-Calculus Blackline Masters, Advanced Math – Pre-Calculus Page 1 Louisiana Comprehensive Curriculum, Revised 2008 ® Most of the math symbols in this document were made with Math Type software. Specific fonts must be installed on the user’s computer for the symbols to be read. It is best to use the pdf format of a document if a printed copy is needed. To copy and paste from the Word document, download and install the Math ® Type for Windows Font from http://www.dessci.com/en/dl/fonts/default.asp on each computer on which the document will be used. Unit 1, Pre-test Functions Pre-test Functions Name_________________________________ 1. Given f(x) = x2 – x a) Find f(3) _________ b) Find f(x + 1)___ ________________ 2. Find the domain and range for each of the following: a) f(x) = x ___________________ ________________ Domain Range b) g(x) = x – 3 ________________ _________________ Domain Range 1 c) h(x) = ________________ _______________ x Domain Range 3. Write a linear equation in standard form if a) the slope of the line is – ½ and the line passes through (4, -2) ______________________ Blackline Masters, Advanced Math – Pre-Calculus Page 1 Louisiana Comprehensive Curriculum, Revised 2008 Unit 1, Pre-test Functions b) the line passes through the points (5, 4) and (6, 3). ____________________ 3 4. Given f(x) = 2x – 5 and g(x) = x−4 a) Find f(x) + g(x). Write your answer in simplest form. ________________________ b) Find f (x)÷ g(x) ________________________ 5. Given f(x) = x + 3 find f-1(x) ________________________ Blackline Masters, Advanced Math – Pre-Calculus Page 2 Louisiana Comprehensive Curriculum, Revised 2008 Unit 1, Pre-test Functions 6. Find the zeroes of each of the following functions: a) f (x) = x2 − x−2 _________________ b) f (x) = x−3 _________________ 3x 3 7x 7. Solve: + = ________________________ 5 2 10 8. Solve x−2 ≤ 3 Write your answer in interval notation. _________________ Blackline Masters, Advanced Math – Pre-Calculus Page 3 Louisiana Comprehensive Curriculum, Revised 2008 Unit 1, Pre-test Functions 9. Given the graph of y = f(x) below. Over what interval/s is the graph increasing?___________________________ decreasing?________________________ 10. Given the graph of y = f(x) below. Using the same coordinate system sketch y = f(x – 1) + 2 Blackline Masters, Advanced Math – Pre-Calculus Page 4 Louisiana Comprehensive Curriculum, Revised 2008 Unit 1, Pre-test Functions with Answers Name_____Key_____________ 1. Given f(x) = x2 – x a) find f(3) ___6_______ b) find f(x + 1)___x2+x________________ 2. Find the domain and range for each of the following: a) f(x) = x ____{x:x≥0}____ _{y: y ≥ 0}_____ Domain Range b) g(x) = x – 3 ___D:_all reals_______ R: all reals__ Domain Range 1 c) h(x) = __{x: x ≠ 0}_______ __{y: y ≠ 0 }______ x Domain Range 3. Write a linear equation in standard form if a) the slope of the line is – ½ and the line passes through (4, -2) x + 2y = 0 b) the line passes through the points (5, 4) and (6, 3). x + y = 9 3 4. Given f(x) = 2x – 5 and g(x) = x−4 a) Find f(x) + g(x). Write your answer in simplest form. 2x2 −13x+23 x−4 b) Find f (x)÷ g(x) 2x2 −13x+20 3 Blackline Masters, Advanced Math – Pre-Calculus Page 5 Louisiana Comprehensive Curriculum, Revised 2008 Unit 1, Pre-test Functions with Answers 5. Given f(x) = x + 3 find f-1(x) f-1(x) = x – 3 6. Find the zeroes of each of the following functions: a) f (x) = x2 − x−2 _{2, -1}_______ b) f (x) = x−3 _{3}_________ 3x 3 7x 7. Solve: + = ___{15}_____ 5 2 10 8. Solve x−2 ≤ 3 Write your answer in interval notation. ____[-1, 5]___ 9. Given the graph of y = f(x) below. Over what interval/s is the graph b g increasing? (−∞,−3) and 0,∞ decreasing? __(-3, 0)______ 10. Given the graph of y = f(x) below. Using the same coordinate system sketch y = f(x – 1) + 2 Blackline Masters, Advanced Math – Pre-Calculus Page 6 Louisiana Comprehensive Curriculum, Revised 2008 Unit 1, What Do You Know about Functions? Word + ? - What do I know about this topic? function domain range independent variable dependent variable open intervals closed intervals function notation vertical line test implied domain increasing intervals Blackline Masters, Advanced Math – Pre-Calculus Page 7 Louisiana Comprehensive Curriculum, Revised 2008 Unit 1, What Do You Know about Functions? decreasing intervals relative maximum relative minimum local extrema even function odd function translations zeros reflections dilations one-to-one Blackline Masters, Advanced Math – Pre-Calculus Page 8 Louisiana Comprehensive Curriculum, Revised 2008