source : socratic.org

## How are the graphs f(x)=x^3 and g(x)=0.75(x+1)^3 related?

#f(x)# is what we call the parent function. Let’s see what #x^3# looks like:

graph{x^3 [-10, 10, -5, 5]}

Now let’s see what #(x+1)^3# looks like:

graph{(x+1)^3 [-10, 10, -5, 5]}

You should see that it’s just a shifted version of the parent function. In this case, it’s a horizontal shift #1# unit to the left.

Now, let’s see what the constant in the function does. Since it’s hard to see what’s going on if we use #0.75#, let’s graph another function that will tell us what a constant THAT is LESS THAN #1# does. Let’s look at #0.1(x+1)^3#

graph{0.1(x+1)^3 [-10, 10, -5, 5]}

You should see that the constant is the #y#-intercept – the value when it crosses the #x# axis.

Function (mathematics) – Wikipedia – Functions were originally the idealization of how a varying quantity depends on another quantity. The red curve is the graph of a function, because any vertical line has exactly one crossing point with the curve. A function that associates any of the four colored shapes to its color.O C. The Graph Of G(x) Is The Graph Of X) Reflected In The X Axis And Shifted O D. The Graph Of G(x) Is The Graph Of F(x) Shited Down 5 Units Choose The Correct Graph Below OA. Transcribed Image Text from this Question. How is g(x) related to f(x)?a student graphed f(x)=x and g(x)=f(x) 3 on the same coordinate grid. Describe, in words, how the graphs of f and g are related. Transformations, I need help please!!!

Solved: How Is G(x) Related To F(x)? O A. The Graph… | Chegg.com – Reflections of Functions: -f (x) and f (-x). Reflection over the x-axis. -f (x) reflects f (x) over the x-axis. Hint: To remember which way to move the graph, set (x + k) = 0. The solution will tell you in which direction to move and by how much. f (x – 2): x – 2 = 0 gives x = +2, move right 2 units. f (x + 3)…Shifting functions examples. This is the currently selected item. so we have these two graphs that looks pretty similar y equals f of X and y is equal to G of X and what they ask us to do is write a formula for the function G in terms of F so let's think about how to do it and like always pause the video and……functions for which g(x) = f(x – 3) for all values of x. a. How are the graphs of f(x) and g(x) related geometrically? b. If f(x) has a local minimum at (-4, -2) and a local maximum at (3 4 Find the rule for the function g(x) whose graph is the image of the graph of f(x) under the indicated transformations.

a student graphed f(x)=x and g(x)=f(x) 3 on… | Wyzant Ask An Expert – Write the quadratic function in the form y = a(x – h) ² + k that is described by the sentence below. Performance Task week 8Directions: Select 3 quadratic functions above and Sketch their graphs on theCartesian coordinate plane below. Label the graph … with the function it represents.graph gx is the reflection of graph fx and then transformed 1 unit down. Yes, the integral of gx dx is g integral x dx. In this case, g is unrelated to x, so it can be treated as constant and pulled outside of the integration.We can imagine that during the process of transformation an even function eats up the negative sign of the variable while the odd function releases the negative sign of the variable. Therefore f∘g is even. Do this for all four possible combinations and you'll see how things work.