Questions
Questions
Single choice

A graph of the function with equation [math: y=sin(x)] is transformed by- a dilation of factor 2 from the [math: y] -axis - a translation of [math: π3] \frac{ \pi }{3} units in the negative direction of the [math: x] -axis- a translation of 1 unit in the negative direction of the [math: y] -axisThe equation of the image is given by:

Options
A.A. [math: y=2sin((x+π3))+1] y=2sin( (x+ \frac{ \pi }{3} ))+1
B.B. [math: y=2sin((x+π3))−1] y=2sin( (x+ \frac{ \pi }{3} ))-1
C.C. [math: y=sin(12(x−π3))−1] y=sin( \frac{1}{2} (x- \frac{ \pi }{3} ))-1
D.D. [math: y=sin(12(x+π3))−1] y=sin( \frac{1}{2} (x+ \frac{ \pi }{3} ))-1
View Explanation

View Explanation

Verified Answer
Please login to view
Step-by-Step Analysis
We start by clearly restating the problem and the available options to ensure we follow the intended transformations correctly. Question and options restated: - The original graph is y = sin(x). - Transformations applied: (1) a dilation of factor 2 from the y-axis, (2) a translation left by π/3, (3) a translation downward by 1 unit. - The answer choices are: A. y = 2 sin((x + π/3)) + 1 B. y = 2 sin((x + π/3)) − 1 C. y = sin(1/2 (x − π/3)) − 1 D. y = sin(1/2 (x + π/3)) − 1 Option-by-option analysis: Option A: y = 2 sin((x + π/3)) + 1 - This option applies a vertical stretch by a factor of 2 (which matches the dilation b......Login to view full explanation

Log in for full answers

We've collected over 50,000 authentic exam questions and detailed explanations from around the globe. Log in now and get instant access to the answers!

Similar Questions

Question textThe circular function [math: f(x)=sin(x)] has been dilated in the [math: y] axis direction by a factor [math: 3]\displaystyle {3}, translated [math: π3]\displaystyle {\frac{\pi}{3}} units in the positive direction of the [math: x] axis and translated [math: 8]\displaystyle {8} units in the negative direction of the [math: y] axis. The resulted function is [math: f(x)]=[input] Check Question 1

Question textThe circular function [math: f(x)=sin(x)] has been dilated in the [math: y] axis direction by a factor [math: 6]\displaystyle {6}, translated [math: 2π3]\displaystyle {\frac{2\,\pi}{3}} units in the positive direction of the [math: x] axis and translated [math: 6]\displaystyle {6} units in the negative direction of the [math: y] axis. The resulted function is [math: f(x)]=[input] Check Question 1

Question textThe circular function [math: f(x)=sin(x)] has been dilated in the [math: y] axis direction by a factor [math: 4]\displaystyle {4}, translated [math: π4]\displaystyle {\frac{\pi}{4}} units in the positive direction of the [math: x] axis and translated [math: 7]\displaystyle {7} units in the negative direction of the [math: y] axis. The resulted function is [math: f(x)]=[input] Check Question 1

Question textThe circular function [math: f(x)=sin(x)] has been dilated in the [math: y] axis direction by a factor [math: 4]\displaystyle {4}, translated [math: π4]\displaystyle {\frac{\pi}{4}} units in the positive direction of the [math: x] axis and translated [math: 7]\displaystyle {7} units in the negative direction of the [math: y] axis. The resulted function is [math: f(x)]=[input] Check Question 1

More Practical Tools for Students Powered by AI Study Helper

Join us and instantly unlock extensive past papers & exclusive solutions to get a head start on your studies!