The graph of the function is attached in [tex]\boxed{{\mathbf{Figure 1}}}[/tex].
Further explanation:
Sine function:
A function is relation between two and more than two variables that assigns exactly one output to each input.
The main trigonometric functions are the sine, cosine and tangent has the input of an angle that is written in degrees or radians.
The output value of the sine function lies between where the input values (angles) are from [tex]0{\text{ to }}2\pi[/tex].
The sine function is written as [tex]\sin \left( x \right)[/tex] in which [tex]x[/tex] is the independent variable.
Inverse of sine function:
The inverse of any function is the reversed rule in which defined input become output and output becomes input.
The inverse of the sine function is known as [tex]{\text{arcsin}}\left( x \right)[/tex]
The inverse function always assign one output to each input as the inverse only exists when the function is one-one and onto.
It can be check through horizontal line test in which we draw a horizontal line that passes through the function.
Function transformation:
A function can be transformed by shifting upward, downward, leftward and rightward.
The function shifts upward when the number is added in the basic function and shifts downward when the number is subtracted from the basic function.
The function [tex]g\left( x \right) = f\left( x \right) + b[/tex] can be graphed by the shifting of [tex]b[/tex] in the upward direction of [tex]f\left( x \right)[/tex] where [tex]f\left( x \right)[/tex] is the basic function and the another function [tex]h\left( x \right) = f\left( x \right) - b[/tex] can be graphed by the shifting of [tex]b[/tex] in the downward direction of [tex]f\left( x \right)[/tex].
The given function is [tex]a\sin x + 15[/tex] where [tex]a\sin x[/tex] is the inverse of sine function.
The graph of the function [tex]a\sin x + 15[/tex] can be drawn by the following steps.
Step by step explanation:
Step 1:
Consider the function [tex]a\sin x + 15[/tex] as [tex]g\left( x \right)[/tex] in which the basic function is [tex]a\sin x[/tex].
Therefore, the function is [tex]f\left( x \right) = a\sin x[/tex] and [tex]g\left( x \right) = a\sin x + 15[/tex].
Step 2:
The function [tex]g\left( x \right) = a\sin x + 15[/tex] can be graphed by shifting upward of 15 units in the function [tex]f\left( x \right) = a\sin x[/tex].
The function is drawn in the attached Figure 1.
Learn more:
- Learn more about the function is graphed below https://brainly.com/question/9590016
- Learn more about the symmetry for a function https://brainly.com/question/1286775
- Learn more about midpoint of the segment https://brainly.com/question/3269852
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Functions
Keywords: Inverse function, transformation, sine, shifting, upward, addition, subtraction, trigonometric function, output value, reversed rule, basic function, horizontal line test.
