Answer: The correct conclusion is(B) The functions f(x) and g(x) are reflections over the y-axis.
Step-by-step explanation: Two functions f(x) and g(x) are given as follows:
We know that if f(-x) = g(x), then the functions are reflections over Y-axis and if - f(x) = g(x), then the functions are reflections over X-axis.
We have,
So, the function g(x) is a reflection of f(x) over Y-axis.
The graph of f(x) and g(x) are drawn in the attached file. From there, it is clear that the functions are reflections over Y-axis, not reflections over X-axis.
So, options (A) is incorrect and option (B) is correct.
From the table, we have
So, as the value of 'x' increases, the value of f(x) increases and value of y(x) decreases.
Therefore, f(x) is an increasing function and g(x) is a decreasing function. So, option (C) is incorrect.
Also, we have
So, both the functions have same initial value. So, option (D) is also incorrect.
Thus, the correct conclusion is (B) The functions f(x) and g(x) are reflections over the y-axis.
Answer: (4,2)
Step-by-step explanation:
When a point is reflected over the x axis, only the x value changes to the opposite sign (positive or negative). The y value doesn’t change.
Answer:
I. Hijo, h = 10 años
II. Padre, P = 40 años
Step-by-step explanation:
- Sea la edad del padre P.
- Sea la edad del hijo h.
Traduciendo el problema verbal a una expresión algebraica, tenemos;
P = 4h .....ecuación 1.
P + 5 = 3(h + 5) ........ecuación 2.
Simplificando aún más, tenemos;
P + 5 = 3h + 15
P = 3h + 15 - 5
F = 3h + 10 ......ecuación 3.
Sustituyendo la ecuación 1 en la ecuación 3;
4h = 3h + 10
4h - 3h = 10
<em>h = 10 años </em>
A continuación, encontraríamos la edad del padre;
P = 4h
P = 4 * 10
<em>P = 40 años</em>
Let's say the point is C, so C partitions AB into two pieces, where AC is at a ratio of 3 and CB is at a ratio of 7, thus 3:7,
Answer:
x ≥ 7
Step-by-step explanation:
|x - 7| = x - 7
A. For each absolute, find the intervals
x - 7 ≥ 0 x - 7 < 0
x ≥ 7 x < 7
If x ≥ 7, |x - 7| = x - 7 > 0.
If x < 7, |x - 7| = x - 7 < 0. No solution.
B. Solve for x < 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
-x + 14 = x
14 = 2x
x = 7
7 ≮7. No solution
C. Solve for x ≥ 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
True for all x.
D. Merge overlapping intervals
No solution or x ≥ 7
⇒ x ≥ 7
The diagram below shows that the graphs of y = |x - 7| (blue) and of y = x - 7 (dashed red) coincide only when x ≥ 7.
