本题目来源于试卷: Trigonometric Functions，类别为 IB数学
[问答题]
Consider the function f(x)=sin x , f l:rf 1yg3u2zda5xae hwi)h j43yw:zbbs;+k2or poume.k7ow 1-2v 4 k*w*zbiuh $x \in \mathbb{R}$ , where x is in radians.
1. Write down:
1. the maximum value of f ;
2. the smallest positive value of x for which the maximum of f occurs.
Let $g(x)=2 \sin \left(x+\frac{\pi}{4}\right)$ , for $ x \in \mathbb{R}$ , where x is in radians.
2. 1. Determine the two transformations the graph of f undergoes to form the graph of g .
2. Hence find the maximum value of g and the smallest positive value of x for which this maximum occurs.
Let $h(x)=\frac{4}{2 \sin \left(x+\frac{\pi}{4}\right)-3}$, for $x \in \mathbb{R}$, where x is in radians.
3. Determine if the graph of h has a vertical asymptote. Justify your answer.
4. Find the range of h .
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