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Problem 127

Sketch the graph of \(f(x)=x^{3}\) and the graph of the function \(g .\) Describe the transformation from \(f\) to \(g .\) $$g(x)=(x-1)^{3}$$

Problem 127

Find the exact value of each function for the given angle for \(f(\theta)=\sin \theta\) and \(g(\theta)=\cos \theta .\) Do not use a calculator. (a) \((f+g)(\theta)\) (b) \((g-f)(\theta)\) (c) \([g(\theta)]^{2}\) (d) \((f g)(\theta)\) (e) \(f(2 \theta)\) (f) \(g(-\boldsymbol{\theta})\) $$\theta=7 \pi / 6$$

Problem 128

Find the exact value of each function for the given angle for \(f(\theta)=\sin \theta\) and \(g(\theta)=\cos \theta .\) Do not use a calculator. (a) \((f+g)(\theta)\) (b) \((g-f)(\theta)\) (c) \([g(\theta)]^{2}\) (d) \((f g)(\theta)\) (e) \(f(2 \theta)\) (f) \(g(-\boldsymbol{\theta})\) $$\theta=5 \pi / 6$$

Problem 128

Sketch the graph of \(f(x)=x^{3}\) and the graph of the function \(g .\) Describe the transformation from \(f\) to \(g .\) $$g(x)=x^{3}-4$$

Problem 129

Find the exact value of each function for the given angle for \(f(\theta)=\sin \theta\) and \(g(\theta)=\cos \theta .\) Do not use a calculator. (a) \((f+g)(\theta)\) (b) \((g-f)(\theta)\) (c) \([g(\theta)]^{2}\) (d) \((f g)(\theta)\) (e) \(f(2 \theta)\) (f) \(g(-\boldsymbol{\theta})\) $$\theta=4 \pi / 3$$

Problem 129

Sketch the graph of \(f(x)=x^{3}\) and the graph of the function \(g .\) Describe the transformation from \(f\) to \(g .\) $$g(x)=2-x^{3}$$

Problem 130

Find the exact value of each function for the given angle for \(f(\theta)=\sin \theta\) and \(g(\theta)=\cos \theta .\) Do not use a calculator. (a) \((f+g)(\theta)\) (b) \((g-f)(\theta)\) (c) \([g(\theta)]^{2}\) (d) \((f g)(\theta)\) (e) \(f(2 \theta)\) (f) \(g(-\boldsymbol{\theta})\) $$\theta=-5 \pi / 3$$

Problem 130

Sketch the graph of \(f(x)=x^{3}\) and the graph of the function \(g .\) Describe the transformation from \(f\) to \(g .\) $$g(x)=-(x+3)^{3}$$

Problem 131

Find the exact value of each function for the given angle for \(f(\theta)=\sin \theta\) and \(g(\theta)=\cos \theta .\) Do not use a calculator. (a) \((f+g)(\theta)\) (b) \((g-f)(\theta)\) (c) \([g(\theta)]^{2}\) (d) \((f g)(\theta)\) (e) \(f(2 \theta)\) (f) \(g(-\boldsymbol{\theta})\) $$\theta=-270^{\circ}$$

Problem 131

Sketch the graph of \(f(x)=x^{3}\) and the graph of the function \(g .\) Describe the transformation from \(f\) to \(g .\) $$g(x)=(x+1)^{3}-3$$

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