Troubles with some math Translations

[Lorax]

Hey I'm having a few troubles with some Translations if anyone could help me out.


15. The graph of y=f(x). where f(x) = |x+4| + 1, its reflected in the y axis. This produces the same results as would translating the graph of y=f(x) to the right by how many units?

I was sick for a bit so I sort of forget or am unsure of how you'd figure that out. Essentially what does |x+4| + 1 look like? Is it a prabola or a straight line sort of deal. I think after that reminder I could manage.

Okay and here's a few more... They have pics so it might be hard... so I'll try and simplify.

if y=f(x^2) -3 what does y=1/f(x^2) -3 look like? Its multiple choice but its hard to explain since they are in picture format. What happens to parabola's when they are 1/f(x)?

Thanks

 

[HallsofIvy]

f(x)= |x+4| is a "bent" straight line. It is the straight line through (0,4) and (-4,0) to the right of x=-4 and then "bends" to go through (-5, 1) again.

f(x)= |x+4|+ 1 is that moved up 1.

Reflecting in the y-axis changes x to -x so (-4,1) to (4,1), same as translating 8 places to the right.

 

[tacman]

for reaching out for help with your math translations troubles. In order to help you, I will explain the concept of reflections and translations in graphs, and then provide an explanation for the specific problems you mentioned.

Firstly, when we reflect a graph in the y-axis, it means that we are flipping the graph over the y-axis. This means that any point (x,y) on the original graph will now be at (-x,y) on the reflected graph. Essentially, we are just changing the sign of the x-coordinate.

Now, when we translate a graph to the right by a certain number of units, we are shifting the graph horizontally to the right by that number of units. This means that any point (x,y) on the original graph will now be at (x-k,y) on the translated graph, where k is the number of units we are shifting to the right.

In the first problem, the function is given as y=f(x) where f(x)=|x+4|+1. This function is a V-shaped graph, known as an absolute value function. When we reflect this graph in the y-axis, it will still maintain its V-shape, but will be flipped over the y-axis. This means that the function will now be y=f(-x) where f(x)=|x-4|+1. To translate this graph to the right, we need to shift the x-coordinate by 4 units, so the function will now be y=f(-x+4), which is equivalent to y=f(-(x-4)). This means that the graph is translated to the right by 4 units.

In the second problem, the function is given as y=f(x^2)-3. This function is a parabola, and when we take the reciprocal of this function, we are essentially flipping the graph over the x-axis. This means that the function will now be y=1/f(x^2)-3, which is equivalent to y=1/f(-x^2)-3. This means that the graph is reflected in the x-axis. The function y=1/f(x^2)-3 will still be a parabola, but the vertex will now be at (0,-3), and the graph will open downwards instead of upwards.

I hope this helps with your understanding of these math translations. If you have any further questions, don't hesitate to ask. Good luck with your studies!