Translations of graphs

Describe the transformation from $f\left(x\right)$ to $g\left(x\right)$ for $g\left(x\right)=-f\left(x\right)$

A reflection in the $x$-axis (All the $y$ values change their sign)

Describe the transformation from $f\left(x\right)$ to $g\left(x\right)$ for $g\left(x\right)=f\left(-x\right)$

A reflection in the $y$-axis (All the $x$ values change their sign)

Describe the transformation from $f\left(x\right)$ to $g\left(x\right)$ for $g\left(x\right)=f\left(x\right)+c$

A translation up the $y$-axis by c units (All the $y$ values increase by $c$)

Describe the transformation from $f\left(x\right)$ to $g\left(x\right)$ for $g\left(x\right)=f\left(x\right)-c$

A translation down the $y$-axis by c units (All the $y$ values decrease by $c$)

Describe the transformation from $f\left(x\right)$ to $g\left(x\right)$ for $g\left(x\right)=f\left(x+c\right)$

A translation left along the $x$-axis by c units (All the $x$ values decrease by $c$)

Describe the transformation from $f\left(x\right)$ to $g\left(x\right)$ for $g\left(x\right)=f\left(x-c\right)$

A translation right along the $x$-axis by c units (All the $x$ values increase by $c$)

P is a point of the function $f(x)$ at (1,4). What are the coordinates of the new position of P when the $f(x)$ is transformed to $-f(x)$

$$(1,-4)$$

P is a point of the function $f(x)$ at (1,4). What are the coordinates of the new position of P when the $f(x)$ is transformed to $f(-x)$

$$(−1, 4)$$

P is a point of the function $f(x)$ at (1,4). What are the coordinates of the new position of P when the $f(x)$ is transformed to $f(x)+2$

$$(1, 6)$$

P is a point of the function $f(x)$ at (1,4). What are the coordinates of the new position of P when the $f(x)$ is transformed to $f(x)-7$

$$(1, -3)$$

P is a point of the function $f(x)$ at (1,4). What are the coordinates of the new position of P when the $f(x)$ is transformed to $f(x+7)$

$$(-6,4)$$

P is a point of the function $f(x)$ at (1,4). What are the coordinates of the new position of P when the $f(x)$ is transformed to $f(x-4)$

$$(5, 4)$$

$f(x)$ is a translation of $x²$. Describe $f(x)$ as a quadratic equation in completed the square form.

$$f(x)=(x-2)²-5$$

$f(x)$ is the blue curve. Describe the orange curve $g(x)$ in terms of $f(x)$

$$g(x)=f(x)-2$$

$f(x)$ is the blue curve. Describe the orange curve $g(x)$ in terms of $f(x)$

$$g(x)=f(-x)$$

$f(x)$ is the blue curve. Describe the orange curve $g(x)$ in terms of $f(x)$

$$g(x)=f(x+2)$$

$f(x)$ is the blue curve. Describe the orange curve $g(x)$ in terms of $f(x)$

$$g(x)=-f(x)$$

$f(x)$ is the blue curve. Describe the orange curve $g(x)$ in terms of $f(x)$

$$g(x)=f(x)+4$$

$f(x)$ is the blue curve. Describe the orange curve $g(x)$ in terms of $f(x)$

$$g(x)=f(x-3)$$

$f(x)$ is the blue curve. Describe the orange curve $g(x)$ in terms of $f(x)$

$$g(x)=-f(x+1)$$

$f(x)$ is the blue curve. Describe the orange curve $g(x)$ in terms of $f(x)$

$$g(x)=f(x-2)+3$$

$f(x)$ is a translation of $x²$. Describe $f(x)$ as a quadratic equation in completed the square form.

$$f(x)=(x+4)²+1$$