Question

Given that
()=2(−3)2−8
f
(
x
)
=
2
(
x
−
3
)
2
−
8
, determine the true statement.



The x intercepts of the graph of f(x) are (1,0) and (5,0).





Group of answer choices

The range of f(x) is
≥−8
y
≥
−
8
.

The graph of f(x) is decreasing from
(3,∞)
(
3
,
∞
)
.

The graph of f(x) has a maximum point at (3, -8).

The domain of f(x) is
≥3
x
≥
3

Answer 1

Equations are used to show the relationship between variables (usually x and y). The true statement about f(x) is that the range of f(x) is $y \ge -8$

Given that:

$f(x) = 2(x - 2)^2 - 8$

To identify the true statement, I will make use of graphical method.

See attachment for the graph of $f(x) = 2(x - 2)^2 - 8$

From the attached graph, we can see that the graph as a minimum at:

$(x,y) = (2,-8)$

And it opens upward.

This implies that the minimum y-value of f(x) is at -8, and it has no maximum.

In other words, the range of the function is:

$f(x) \ge -8$

Hence, the true statement is option (a):

The range of f(x) is $y \ge -8$

Read more about equations at:

https://brainly.com/question/17995541