Answer:
C. Up.
Step-by-step explanation:
We have been given that the parent function is transformed to the function
. We are asked to describe the given transformation.
Let us recall the transformation rules.
,
,
,
.
Upon comparing our transformed function with the parent function, we can see that the graph is shifted to left by 7 units and upwards by 5 units.
Therefore the correct choice is option C.
Zeroes:
We must solve
To do so, we define the auxiliary variable . The equation becomes
The quadratic formula yields the solutions
Substituting back gives
So, the zeroes are -6, -3, 3, 6.
Turning points:
Turning points are points where a function stops being increasing to become decreasing, or vice versa. Since functions are increasing when their first derivative is positive and decreasing when it's negative, turning points are points where the first derivative is zero.
We have
If we set the derivative to be zero, we have
So, the derivative is zero if x=0 or
