Part of the graph of the function f(x) = (x + 4)(x – 6) is shown below. Which statements about the function are true? Select two
options. The vertex of the function is at (1,–25). The vertex of the function is at (1,–24). The graph is increasing only on the interval −4< x < 6. The graph is positive only on one interval, where x < –4. The graph is negative on the entire interval –4 < x < 6.
2 answers:
Answer:
The vertex of the function is at (1,–25)
The graph is negative on the entire interval -4 < x < 6
Step-by-step explanation:
we have
This is a vertical parabola open upward
The vertex is a minimum
using a graphing tool
see the attached figure
The vertex is the point (1,-25)
The x-intercepts or roots of the quadratic function are x=-4, x=6
The graph is increasing on the interval x > 1
The graph is decreasing on the interval x < 1
The graph is positive on two intervals ,where x < -4 and x > 6
The graph is negative on the entire interval -4 < x < 6
therefore
The statements that are true are
The vertex of the function is at (1,–25)
The graph is negative on the entire interval -4 < x < 6
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The correct equation matches the set of ordered pairs of functions:
<u><em>C.f (0) = 6 </em></u>
<h3>Further explanation </h3>Set A to set B is said to be a function if each member of set A pairs is exactly one member of set B
So, one value of x is only assigned to one value of y
or <em>it has only one relationship for each input value </em>
A function can be expressed in the form of a cartesian diagram, the set of ordered pairs, or arrow diagram
If y is a function of x, then y = f (x)
where x is the independent variable and y is the dependent variable
x is the domain and y is the result area or range
A function can be write as ordered pair
Ordered pairs because we write the input first, and then the output
Can be described in form
<h3>(input, output) </h3><em>or </em>
So A function can be formed as a set of ordered pairs:
For example a set of ordered pairs
- (2,4), (3,5), (4,6)
input values (as domain) 2,3,4
output values (as range) 4,5,6.
We complete the questions with answer choices :
The function f (x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)}:Which equation is true?
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
Let see the answer choices :
- f (-10) = 1
values x = -10, f (x) = y = 1, ordered pairs (-10,1)
- f (2) = - 10
values x = 2, f (x) = y = -10, ordered pairs (2, -10)
- f (0) = 6
value x = 0, f (x) = y = 6, ordered pairs (0.6)
- f (1) = - 10
values x = 1, f (x) = y = -10, ordered pairs (1, -10)
So the answer choices that correspond to the set of ordered pairs of functions above are choices C.f (0) = 6
<h3>Learn more </h3>
F (x) = x2 + 1 g (x) = 5 - x
the inverse of the function f (x) = 2x-10
domain of the function
Keywords: domain, function, the set of ordered pairs, input, output
