1) For which of the following functions is f(-5) = 2 ? a)f(x) = x +7 b) f(x) = 2x-6 c) f(x) = 3x+5 d) none of these
2) Which of the following is a function? a)(-4,1), (1,8), (-4,2) b)(-4,1), (1,-8), (-2,2) c)(-4,1),(1,-8), (1,2) d) none of these
3) what is the relationship between the lines y=-8x +5 and y =-3x -7 ?
4) evaluate i^14
I think
1- a
2- don't understand
3 -don't understand
4 - -1
can someone veridy & assist me on this ?
1. correct
4. correct
2.
A function is a relation which relates the elements of two sets (of numbers) such that any element of the first set is related to exactly one element of the second set.
For example:
A={1,2,3}, B={4,5,6}
f: A->B is a function which relates elements of set A to elements of set B.
If we define f by (1,4),(2,6),(3,5), then the relation f is a function, since it satisfies the stipulation that any element in A is related to exactly one element in B.
On the other hand,
if we define:
g : A-> B such that
(1,4),(1,6),(2,5),
then g is not a function because element 1 of set A is related to two elements of B (4 and 6). So in this case, g is not a function.
3. The two lines are not parallel, so they intersect somewhere in space.
They are not parallel because the slopes are different (8 and -3).
Sure! Let me help you out.
1) To find which function has f(-5) = 2, we need to substitute x = -5 into each of the given functions and see which one equals 2.
a) f(x) = x + 7
Substituting x = -5: f(-5) = (-5) + 7 = 2
b) f(x) = 2x - 6
Substituting x = -5: f(-5) = 2(-5) - 6 = -10 - 6 = -16
c) f(x) = 3x + 5
Substituting x = -5: f(-5) = 3(-5) + 5 = -15 + 5 = -10
Since only option a) gives f(-5) = 2, the correct answer is a) f(x) = x + 7.
2) A function is a relationship that maps each input value (x) to a unique output value (y). In other words, each x-value can only have one corresponding y-value. To determine if a set of points represents a function, we need to check if there are any repeated x-values.
a) (-4, 1), (1, 8), (-4, 2)
Here, (-4) appears twice as an x-value, so this is not a function.
b) (-4, 1), (1, -8), (-2, 2)
No repeated x-values, so this is a function.
c) (-4, 1), (1, -8), (1, 2)
Here, (1) appears twice as an x-value, so this is not a function.
Therefore, the correct answer is b) (-4, 1), (1, -8), (-2, 2).
3) To determine the relationship between the lines y = -8x + 5 and y = -3x - 7, we can compare their slopes and y-intercepts. The slope of a line represents its steepness, while the y-intercept is the point where the line crosses the y-axis.
Both equations are in slope-intercept form (y = mx + b), where "m" is the slope and "b" is the y-intercept.
For y = -8x + 5, the slope is -8 and the y-intercept is 5.
For y = -3x - 7, the slope is -3 and the y-intercept is -7.
Comparing the slopes, we can see that -8 and -3 are different. This tells us that the lines are not parallel.
Comparing the y-intercepts, 5 and -7 are different. This tells us that the lines intersect at some point.
Therefore, the relationship between the lines y = -8x + 5 and y = -3x - 7 is that they intersect at a certain point.
4) To evaluate i^14, we need to understand that i is defined as the imaginary unit, where i^2 = -1. By repeatedly applying the definition, we can simplify the expression.
i^2 = -1
i^4 = (i^2)^2 = (-1)^2 = 1
i^6 = i^4 * i^2 = 1 * -1 = -1
i^8 = (i^4)^2 = 1^2 = 1
i^10 = i^8 * i^2 = 1 * -1 = -1
i^12 = (i^4)^3 = 1^3 = 1
i^14 = i^12 * i^2 = 1 * -1 = -1
Therefore, i^14 = -1.
I hope this clarifies your doubts and verifies your answers! Let me know if there's anything else I can assist you with.