Let f(x)=x3 and g(x)=x − 3. a) Determine the equations of the composite functions (f ∘ g)(x) and (g ∘ f)(x). b) Graph the composite functions. c) Graph the composite functions. Describe (f ∘ g)(x) and (g ∘ f)(x) as transformations of f(x).

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Let f(x)=x3 and g(x)=x − 3. a) Determine the equations of the composite functions (f ∘ g)(x) and (g ∘ f)(x). b) Graph the composite functions. c) Graph the composite functions. Describe (f ∘ g)(x) and (g ∘ f)(x) as transformations of f(x).

jlo2niT · Accepted Answer

Step 1 Given: f(x)=x3 g(x)=x − 3 a) Let us use the definition of composite functions (f ∘ g)(x)=f(g(x)) along with the definitions of f and g to determine the composite functions. (f ∘ g)=f(g(x))=f(x − 3)=(x − 3)3 (g ∘ f)(x)=g(f(x))=f(x3)=x3 − 3  Step 2 b) We need to graph the two functions (f ∘ g)(x)=(x − 3)3 and (g ∘ f)(x)=x3 − 3. For a TI8384−calca―→r, press Y=, then enter (X − 3)3 afterY1  and enter X^{3 - 3} after Y2. Next, press GRAPH to graph the two curves.  Step 3 c) A function of the form g(x)=a f(b(x + c)) + d is obtained by stretching the function f(x) vertically by a factor a(a &amp;lt; 0 flips the function uψde down), stretching the function horizontally by a factor b(b &amp;lt;0 flips the graph ≤ft−),moves the function to the left by c units (→ the right when c &amp;lt; 0) and moves the function up by d units (down when d &amp;lt; 0). We note that the function

Let f(x)=x^{3} and g(x)=x - 3. a) Determine the equations of the composite functions (f circ g)(x) and (g circ f)(x). b) Graph the composite functions. c) Graph the composite functions. Describe (f circ g)(x) and (g circ f)(x) as transformations of f(x).

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