if you transform a function f(x)=√x into g(x)=f(x+1)−4, how would the graph change? how would the table of…

if you transform a function f(x)=√x into g(x)=f(x+1)−4, how would the graph change? how would the table of values with point coordinates change? it would move up 4 and right 1: y - values increase by 4, x - values increase by 1. it would move down 4 and left 1: y - values decrease by 4, x - values decrease by 1. it would move right 4 and up 1: y - values increase by 1, x - values increase by 4. it would move left 4 and down 1: y - values decrease by 1, x - values decrease by 4.

if you transform a function f(x)=√x into g(x)=f(x+1)−4, how would the graph change? how would the table of values with point coordinates change? it would move up 4 and right 1: y - values increase by 4, x - values increase by 1. it would move down 4 and left 1: y - values decrease by 4, x - values decrease by 1. it would move right 4 and up 1: y - values increase by 1, x - values increase by 4. it would move left 4 and down 1: y - values decrease by 1, x - values decrease by 4.

Answer

Explanation:

Step1: Recall function transformation rules

For a function (y = f(x)), (y=f(x + h)) shifts the graph horizontally (left if (h>0), right if (h < 0)), and (y=f(x)+k) shifts the graph vertically (up if (k>0), down if (k < 0)). For (g(x)=f(x + 1)-4), compared to (y = f(x)):

  • The (x+1) inside the function: Using the rule (y=f(x + h)), when (h = 1), the graph of (y = f(x)) shifts left by (1) unit.
  • The (-4) outside the function: Using the rule (y=f(x)+k), when (k=-4), the graph of (y = f(x)) shifts down by (4) units.

Answer:

It would move left 4 and down 1: y - values decrease by 1, x - values (This option is incorrect as per transformation rules). It would move right 4 and up 1: y - values increase by 1, x - values increase by 4 (This option is incorrect as per transformation rules). It would move down 4 and left 1: y - values decrease by 4, x - values decrease by 1 (This option is correct as per (g(x)=f(x + 1)-4) transformation rules). It would move up 4 and right 1: y - values increase by 4, x - values increase by 1 (This option is incorrect as per transformation rules). So the correct answer is: It would move down 4 and left 1: y - values decrease by 4, x - values decrease by 1.