Question

Which statement correctly describes the relationship between the graph of f(x)=x and the graph of g(x)=f(x+9) ?

The graph of g(x) is the graph of​​​ f(x) translated 9 units right.
The graph of g(x) is the graph of f(x) translated 9 units left.
The graph of g(x) is the graph of​ f(x)​ vertically stretched by a factor of 9.
The graph of g(x) is the graph of​​ f(x)​ vertically compressed by a factor of 9.
3.
The linear parent function, f(x)=x ,was transformed to create a graph g(x) =f(x)−1.

Which statement about the graphs is true?

The graph of f is shifted 1 unit to the left to create the graph of g.
The graph of f is shifted 1 unit down to create the graph of g.
The graph of f is reflected over the x-axis to create the graph of g.
The graph of f is reflected over the y-axis to create the graph of g.
4.
The graph of function g(x) is a vertical stretch of the graph of function f(x)=x ​​by a factor of 2.

Which equation describes function g(x)?

​​g(x)=f(x)−2
​g(x)=12f(x)
g(x)=2f(x)
​​g(x)=f(x)+2
5.
The function f(x)=x was transformed to create a graph g(x)=f(x−3)+1.

Which statement describes how the graphs of f and g are related?

The graph of f is shifted to the right 3 units and down 1 unit to create the graph of g.
The graph of f is shifted to the right 3 units and up 1 unit to create the graph of g.
The graph of f is shifted to the left 3 units and up 1 unit to create the graph of g.
The graph of f is shifted to the left 3 units and down 1 unit to create the graph of g.

Answer 1

I'm not sure with the answer cuz it's s graphic question it can't be explained

Answer 2

Problem 2

Answer: B) Shift 9 units to the left

If we replace every x with x+9, then the inputs are now 9 units larger. This moves the xy axis 9 spaces to the right. If we keep the f(x) curve fixed in place while the xy axis moves, then it gives the illusion f(x) moves 9 units to the left.

====================================================

Problem 3

Answer: B) Shift 1 unit down

Think of f(x) as y. So f(x)-1 means y-1 to show that we subtract 1 from each y coordinate of each (x,y) point on f(x).

====================================================

Problem 4

Answer: C) g(x) = 2f(x)

We multiply each y value by 2. So g(x) = 2y = 2*f(x). This makes f(x) twice as tall as before.

====================================================

Problem 5

Answer: B) shifted to the right 3 units and up 1 unit

The replacement of x with x-3 means we shift 3 units to the right. It's the similar idea to problem 2, but we're working in reverse now.

The +1 at the end means we shift 1 unit up.