Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x − 9)? T
he graph of y = f(x) will shift up 9 units. The graph of y = f(x) will shift down 9 units. The graph of y = f(x) will shift left 9 units. The graph of y = f(x) will shift right 9 units.
1 answer:
Answer:
The graph of y = f(x) will shift to the right 9 units.
Step-by-step explanation:
Despite some lack of clarity, because usually this equality is in terms of x and y. Let's do it.
Taking f(x) as its parent function in other words
Testing some values:
x|y
0|0
1|1
2|2
Adding to the function -9 units is to shift it to the right
Testing some values to certify:
x|y
-9|0-9
-8|1-9
-7|2-9
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Answer:
See the explanation.
Step-by-step explanation:
We are given the function f(x) = x² + 2x - 5
Zeros :
If f(x) = 0 i.e. x² + 2x - 5 = 0
The left hand side can not be factorized. Hence, use Sridhar Acharya formula and
and
⇒ x = -3.45 and 1.45
Y- intercept :
Putting x = 0, we get, f(x) = - 5, Hence, y-intercept is -5.
Maximum point :
Not defined
Minimum point:
The equation can be expressed as (x + 1)² = (y + 5)
This is an equation of parabola having the vertex at (-1,-5) and axis parallel to + y-axis
Therefore, the minimum point is (-1,-5)
Domain :
x can be any real number
Range:
f(x) ≥ - 6
Interval of increase:
Since this is a parabola having the vertex at (-1,-5) and axis parallel to + y-axis.
Therefore, interval of increase is +∞ > x > -1
Interval of decrease:
-∞ < x < -1
End behavior :
So, as x tends to +∞ , then f(x) tends to +∞
And as x tends to -∞, then f(x) tends to +∞. (Answer)