use transformations to describe how the graph of the function is related to a basic inverse trigonometric…
use transformations to describe how the graph of the function is related to a basic inverse trigonometric graph. state the domain and range. h(x)=5tan^(-1)(x/4) describe how the graph of the function is related to a basic inverse trigonometric graph using transformation. select the correct choice below and fill in the answer boxes to complete your choice. (type integers or simplified fractions.) a. to obtain the graph of the given function, stretch horizontally by a factor of and stretch vertically by a factor of b. to obtain the graph of the given function, stretch horizontally by a factor of and shrink vertically by a factor of c. to obtain the graph of the given function, shrink horizontally by a factor of and stretch vertically by a factor of d. to obtain the graph of the given function, translate to the right by units and translate up by units. e. to obtain the graph of the given function, translate to the left by units and translate down by units. f. to obtain the graph of the given function, shrink horizontally by a factor of and shrink vertically by a factor of
Answer
Explanation:
Step1: Recall transformation rules
For a function (y = a\tan^{- 1}(bx)), the horizontal - stretch/shrink and vertical - stretch/shrink rules are considered. The basic inverse - tangent function is (y=\tan^{-1}(x)).
Step2: Analyze horizontal transformation
For the function (h(x)=5\tan^{-1}(\frac{x}{4})), comparing with (y = a\tan^{-1}(bx)), we have (b=\frac{1}{4}). The rule for horizontal transformation of (y = f(bx)) compared to (y = f(x)) is that if (|b|\lt1), the graph of (y = f(x)) is stretched horizontally by a factor of (\frac{1}{|b|}). Here, since (b=\frac{1}{4}), the graph of (y = \tan^{-1}(x)) is stretched horizontally by a factor of (\frac{1}{\frac{1}{4}}=4).
Step3: Analyze vertical transformation
For the function (h(x)=5\tan^{-1}(\frac{x}{4})), we have (a = 5). The rule for vertical transformation of (y=af(x)) compared to (y = f(x)) is that if (|a|>1), the graph of (y = f(x)) is stretched vertically by a factor of (|a|). Here, since (a = 5), the graph of (y=\tan^{-1}(x)) is stretched vertically by a factor of (5).
Answer:
A. To obtain the graph of the given function, stretch horizontally by a factor of (4) and stretch vertically by a factor of (5).