What is the effect on the graph of the function f(x) = x when f(x) is replaced with -1/2 f(x)?
1 answer:
Answer:
C) horizontal reflection over y-axis and horizontal stretch
Step-by-step explanation:
1a- A vertical reflection over the x-axis occurs when a function is transformed into
1b- A horizontal reflection over the y-axis occurs when a function is transformed into
2a- A function is being compressed if is multiplied by a positive factor k:
with
2b- A function is being stretched if is multiplied by a positive factor k:
with
In our problem, the original function is:
- Multiplied by 1/2, so by a factor which is smaller than 1, so we are in case 2b
- Transformed from into
(due to the negative sign in front of it), so we are in case 1b
So, overall, we had a horizontal reflection over the y-axis and a stretch of the function.
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Answer:
f(x)=(x−3)2−5
Find the properties of the given parabola.
Direction:
Vertex: (3,−5)
Focus: (3,−194)
Axis of Symmetry: x=3
Directrix: y=−214
Select a few x
values, and plug them into the equation to find the corresponding y values. The x
values should be selected around the vertex.
x y
1 -1
2 -4
3 -5
4 -4
5 -1
Graph the parabola using its properties and the selected points.
Direction:
Vertex: (3,−5)
Focus: (3,−194)
Axis of Symmetry: x=3
Directrix: y=−214
x y
1 -1
2 -4
3 -5
4 -4
5 -1
Answer:
Congruence between pentagons
Step-by-step explanation:
The relationship occurs because having two congruent Pentagons and generating a segment within them (or outside), congruence is extrapolated to the triangles generated within them. Thus, if there is congruence among the pentagons, it will exist between the formed triangles. In other words since the two pentagons are congruent, the corresponding angle pair is congruent. also the two corresponding side pairs are also congruent.
In the attached image for example, the ABCDE and KLMNO pentagons are congruent, so all of their internal division lines are also congruent (AC and KM)
