Trigonometric and Polar Functions

If a specific tangent function $f(\theta)=6 \tan(\beta \theta)$ is amplified and also reflects across the X-axis, what is one possible expression for this transformation?

What transformation results in a shift upwards by 5 units in the basic Tangent Function, $y = \tan(x)$?

Which value does $\tan(x)$ approach as $x$ approaches $\frac{\pi}{2}$ from the left?

At what x-value within one period is the tangent function equal to zero?

If θ is an angle in standard position, what is tan(θ) when θ = π/4?

If $y=\tan(bx+c)+d$ has a phase shift to the right by $\frac{\pi}{4}$ radians from $y=\tan(bx)$, what should be the value for $c$?

What is an equivalent expression for $\sec^2(x)$, based on trigonometric identities involving the tangent function?

What is the period of the function $f(x)=\tan(3x - \pi)$?

Given that $f(x) = \tan(x)$, where $x$ is measured in radians, at what value of $x$ closest to zero does f^{-1}'(x), represent an instantaneous slope of $-1$?

What quadrants are all values for $\tan(\theta)$, where $\theta$ is an angle in standard position with its terminal side in that quadrant, positive?