If the original function f(x) = 2x2 - 1 is shifted to the left 3 units to make the function g(x), which expression would represent g(x)? (1)2(x-3)^2-1 (3)2x^2+2
(2)2(x+3)^2-1 (4)2x^2-4​

 2(x+3)^2 - 1

To shift the f(x) function 3 units to the left, the xy axis must move 3 units to the right. This effectively means each x input is 3 units larger than before. That's why we replace every x with x+3.

the answers are in the images, i received 100% on this assignment. hope this !

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.