# Grade 11 Math Problem, cant figure out the transformations

• baller2353
In summary, the given problem asks for the graph of y = -2^x + 6, which involves flipping the graph of y = 2^x upside down and shifting it up 6 units. However, the solution shows a graph of y = -2^2x + 6, which is achieved by using a horizontal transformation to get an exponent of 2x in the equation. This is necessary to match the x-intercept shown in the graph.
baller2353

## Homework Statement

the mother graph is y = 2 ^ x

y=2 ^ x

## The Attempt at a Solution

so i know the graph is flipped upsidedown and the whole graph is moved up 6 spots
so i can get y = -2 ^ x + 6

however the solutuion is y =-2 ^2x +6.
i can't seem to figure out how they got the exponent to the exponent 2x. I don't see what horizontal transformations could give you this.

question is in the picture attached.

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baller2353 said:

## Homework Statement

the mother graph is y = 2 ^ x

y=2 ^ x

## The Attempt at a Solution

so i know the graph is flipped upsidedown and the whole graph is moved up 6 spots
so i can get y = -2 ^ x + 6

however the solutuion is y =-2 ^2x +6.
i can't seem to figure out how they got the exponent to the exponent 2x. I don't see what horizontal transformations could give you this.

question is in the picture attached.

Notice that for $$y=-2^x+6$$, it would cut the x-axis at $$x=\log_26=\frac{\ln6}{\ln2}\approx 2.58$$ but from the graph it looks like it's cutting the x-axis at about 1.2 or so, which is about half. Well, how do we get an answer of $$x=\frac{1}{2}\left(\log_26\right)$$ ? Solving backwards we have
$$2x=\log_26$$
$$2^{2x}=6$$
$$2^{2x}-6=0$$

thus we needed an exponent of 2x. Now in an exam or even when solving other questions, you won't go into this much detail, all you need to do is look at where it approximately cuts the x-axis and then use a suitable integer scalar for the exponent (I doubt they'll ever use anything but integers, because it's just not detailed enough).

## 1. What are transformations in Grade 11 Math?

Transformations in Grade 11 Math refer to changes in the position, size, or shape of a geometric figure on a coordinate plane. These changes can be achieved through translation, rotation, reflection, or dilation.

## 2. How do I identify the type of transformation in a problem?

To identify the type of transformation, you need to observe the changes in the coordinates of the vertices of the figure. Translation involves moving the figure without changing its size or shape, rotation involves turning the figure around a fixed point, reflection involves flipping the figure across a line of symmetry, and dilation involves either expanding or shrinking the figure.

## 3. Can you explain how to graph a transformation on a coordinate plane?

To graph a transformation, you need to first plot the original figure on a coordinate plane. Then, use the rules for each type of transformation to determine the new coordinates of the vertices. Finally, connect the new coordinates to create the transformed figure.

## 4. What is the difference between rigid and non-rigid transformations?

Rigid transformations, such as translation and rotation, preserve the shape and size of a figure. Non-rigid transformations, such as reflection and dilation, change the shape and/or size of a figure.

## 5. How can I use transformations to solve real-world problems?

Transformations can be used to solve real-world problems by representing real-life situations as geometric figures on a coordinate plane. By applying the rules for each type of transformation, you can analyze and understand the changes happening in the situation and make predictions or solve for unknowns.

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