Graph of y = f(x)

[solo_guitar]

 

[math_tutor2020]

I'll focus on part (a) only to get you started.
(1,3) is on y = f(x). This means f(1) = 3.
Let's see what happens when we plug x = 1 into the transformed function.
y = f(x+3)-5
y = f(1+3)-5
y = f(4)-5
Uh oh. We run into a problem. The value f(4) is undefined.
So what we need to do is somehow plug in an x value such that x+3 maps to 1
x+3 = 1 solves to x = -2
Let's try x = -2 and we'll see what happens.
y = f(x+3)-5
y = f(-2+3)-5
y = f(1)-5
y = 3-5
y = -2
Therefore the point (-2,-2) is on y = f(x+3)-5
Visually we shifted the point (1,3) five units down and three units left to arrive at (-2,-2)
The -5 at the end means "shift 5 units down", while the x+3 indicates "shift 3 units left".

 

[conway]

Uh oh. We run into a problem. The value f(4) is undefined.
So what we need to do is somehow plug in an x value such that x+3 maps to 1
x+3 = 1 solves to x = -2

Solve for division by zero, and no "shifty" mathematics necessary. Fairly kind response though. Good tutoring.

 

[solo_guitar]

I'll focus on part (a) only to get you started.
(1,3) is on y = f(x). This means f(1) = 3.
Let's see what happens when we plug x = 1 into the transformed function.
y = f(x+3)-5
y = f(1+3)-5
y = f(4)-5
Uh oh. We run into a problem. The value f(4) is undefined.
So what we need to do is somehow plug in an x value such that x+3 maps to 1
x+3 = 1 solves to x = -2
Let's try x = -2 and we'll see what happens.
y = f(x+3)-5
y = f(-2+3)-5
y = f(1)-5
y = 3-5
y = -2
Therefore the point (-2,-2) is on y = f(x+3)-5
Visually we shifted the point (1,3) five units down and three units left to arrive at (-2,-2)
The -5 at the end means "shift 5 units down", while the x+3 indicates "shift 3 units left".

1. Thank you for coming here to help me in my self-study of mathematics.

2. Great reply as always.

3. I look forward to your help along the way.

 

[solo_guitar]

Solve for division by zero, and no "shifty" mathematics necessary. Fairly kind response though. Good tutoring.

He is an amazing math tutor. I invited him here from another site.