You do this by converting to vertex form a(x - b)^2 + c where the axis of symmetry is x = b

the correct function to have a symmetry x = 3 will be the one which includes -6x
which is the last one

x^2 - 6x - 1 = (x - 3)^2 -9-1

the last option is the correct one

3 0

3 years ago

Please help with step by step

gregori [183]

$f(x)=10e^{\frac{x-1}{2}}$

substitute f(x) for y
$y=10e^{\frac{x-1}{2}}$

solve for x

$\frac{y}{10}=e^{\frac{x-1}{2}}$

$ln( \frac{y}{10}) = \frac{x-1}{2}$

$2ln( \frac{y}{10})=x-1$

$2ln( \frac{y}{10})+1 =x$

$2ln( \frac{y}{10})$ is esquivent to $2ln(y) - 2ln(10)$

$2ln(y)-2ln(10)+1=x$

Change x to y and y to x

$2ln(x)-2ln(10)+1=y$

Flip formula and substitute y for g(x)

$g(x)=2ln(x)-2ln(10)+1$

7 0

3 years ago