4. The graph of the function y -x4 is transformed to the graph of the function y

Question

4. The graph of the function y -x4 is transformed to the graph of the function y--[2(r-3)1 by a. a vertical stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up b. a horizontal stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up c, a horizontal compression by a factor of a reflection in the x-axis, a translation of 3 units to the left, and a translation of 1 unit up d.a horizontal compression by a factor of a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up 5. State the equation ofnr) if D = {x e R-3 } and the y-intercept is (0,-2) 2x1 3x+ 2 3x + 2 6. Starting on theitive x-axis and moving 3 ofthe way around a circle that has radius 3 m, how far would one travel? 3.14 m 360 m 6.28 m 0.69 m 7. In which quadrant is the following true? csc ?> 0 and sec ?

Explanation / Answer

4) y = - [ 2 ( x- 3)] ^4 + 1

first is vertical stretch by a factor of 2

reflection over x axis

shifted 3 units to the right

and 1 unit upwards

option a is correct

5) x not equal to 2/3

y intercept ( 0 , -1/2 )

the function f(x) = ( 2x +1 ) / ( 3x - 2)

has y intercept of - 1/2

and x is not equal to 2/3

hence, option a is correct

6) perimeter of circel = 2pi r

= 2 * 3.14 * 3

= 18.84

1/3 of 18.84

= 6.28 m

option c is correct

7) csc theta > 0

sec theta < 0

csc theta = 1/ sin theta

sin theta is positive in 2nd quadrant or 1st quadrant

and sec theta = 1/ cos theta

cos theta is negative in 2nd quadrant

hence, option b is correct

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