1) left 2, down 3
The function is,
Here, the parent function is square root function.
So, Let be the parent function.
Now, in order to transform to , first, we need to add 2 to x and is given by the rule:
. From the transformation rules, if a positive number is added to x, then the graph shifts left.
Hence, the graph of will shift left by 2 units.
Now, next we need to add -3 to to get the given function . The rule is given as:
As per transformation rules, if a negative number is added to the function, the graph shifts down.
Here, the graph of will shift down by 3 units.
Overall, the parent function can be transformed to by shifting the parent function graph 2 units left and 3 units down.
So, option 1 is correct.
right 2, up 3
The given function is
The parent function is
The given transformation is of the form
This is a shift to the right, b units and an upward shift of c units.
is obtained by shift the parent function , 2 units to the right and 3 units up.
The last option is correct.
f^-1 (x) = 1 + 4x^2
right 2 up 3 if the equation is (x-2)+3
Right 2, up 3
In the vertex form transformations
f(x) = a(x-h)²+ka - indicates vertical stretches, compression, and/or a reflection across the x-axis.h - indicates only on the x-axis. Negative = Goes right, Positive - goes leftk - indicates only on the y-axis. Positive = up, negative = down
so we have (x - 3)( x^2 - 25) = 0
So x - 3 = zero and x = therefore = 3.
The answer is the third choice 3
If you meant f(x) = (x-2) + 3, then the graph of f(x) is the same as the graph of g(x) = x+3 translated 2 units to the right.