If f(x)=2sqrt (x-3)+5 is changed to g(x)=-3sqrt (x+4)-1 select all the changes that occurred. x Reflection over the x-axis x Reflection over the y-axis The factor of the vertical stretch increased. x The factor of the vertical stretch decreased. A vertical compression occurred x The function shiffed right 7 units. The function shifted left 7 units. x The function shifted down units 1x 0. The function shifted up 6 units.

To determine the changes that occurred when the function $f(x)$ is changed to $g(x)$, we need to compare the two functions and identify the transformations applied.<br /><br />Given:<br />$f(x) = 2\sqrt{x-3} + 5$<br />$g(x) = -3\sqrt{x+4} - 1$<br /><br />Let's analyze the changes:<br /><br />1. Reflection over the x-axis:<br /> - The coefficient of the square root term in $g(x)$ is negative, indicating a reflection over the x-axis.<br /><br />2. Reflection over the y-axis:<br /> - There is no change in the sign of the variable inside the square root function, so there is no reflection over the y-axis.<br /><br />3. The factor of the vertical stretch increased:<br /> - The coefficient of the square root term in $g(x)$ is -3, which is greater than the coefficient of 2 in $f(x)$. This indicates an increase in the vertical stretch factor.<br /><br />4. The factor of the vertical stretch decreased:<br /> - This is not applicable, as the vertical stretch factor increased.<br /><br />5. A vertical compression occurred:<br /> - This is not applicable, as the vertical stretch factor increased.<br /><br />6. The function shifted right 7 units:<br /> - The variable inside the square root function in $g(x)$ is $x+4$, which is 7 units to the left of $x-3$ in $f(x)$. This indicates a shift of 7 units to the left, not to the right.<br /><br />7. The function shifted left 7 units:<br /> - This is correct. The function shifted left 7 units.<br /><br />8. The function shifted down units:<br /> - The constant term in $g(x)$ is -1, which is 6 units less than the constant term 5 in $f(x)$. This indicates a shift of 6 units down.<br /><br />9. The function shifted up 6 units:<br /> - This is not correct. The function shifted down 6 units.<br /><br />Therefore, the changes that occurred are:<br />- Reflection over the x-axis<br />- The factor of the vertical stretch increased<br />- The function shifted left 7 units<br />- The function shifted down 6 units