Question

4. (5 points each) For function f(1) = 2-*+1+3, (a) Write down the steps of graph transformation from y=2 to f(1). (b) What is the domain and range for f(x)? (c) What is the horizontal asymtote for f(x)? (d) Create a table and evaluate at least three points and sketch the graph of f(x).

Answer 1

te) -1+1 + 3 means means free) = We know that, when f(x) is a function function then f(x) +b fox) chifted a units upward 0 f(x)-b means flx) shifted b cenite downward @ f(x+b) means fla) shifted b units left f(x-b) means fle) shifted bunits right - f(x) fa) reflected in x-axis → fl-x) f(x) reflected in y-asis Given fees = f(-x) = x Reflected about y-aris from @ f(x+1) {-x+1) 1 unit left from ③ shifted Ex+1) fox)+3 means x 2 +3 from are shifted 3 units upward Therefore, transformations Reflected about yrasis shifted 1 unit to the left shifted 3 units upwards. *

16. Domain. The function has no undefined points nor domain constraints. :. Domain is -ocacoo. Interval Notation (-0, 0] Range The range of exponential function of the form. axt6 Cin 'th is f(x) >k K=3 : f(x)>3 . Interval Notation (3,0)) © Asymptote: Horizontal Asymptote: Exponential function of form f(x) = can axtbtk has Horizontal asymptote y=k. K = 3. - Horizontal Asymptote : Y= 3

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