Use the y-intercept B(0; -3) to find q.

The function is $f(x) = p^x + q$. Since B(0; -3) is the y-intercept of $f$, substitute $x=0$ and $f(x)=-3$ into the equation.

$$-3 = p^0 + q$$

Since any non-zero number raised to the power of 0 is 1 ($p^0 = 1$):

$$-3 = 1 + q$$ $$q = -3 - 1$$ $$q = -4$$

Point A(3; 4) is on the graph of $f(x)$. Substitute $x=3$, $f(x)=4$, and $q=-4$ into the equation $f(x) = p^x + q$.

$$4 = p^3 + (-4)$$ $$4 = p^3 - 4$$

Add 4 to both sides:

$$4 + 4 = p^3$$ $$8 = p^3$$

Take the cube root of both sides:

$$p = \sqrt[3]{8}$$ $$p = 2$$

The values are $p=2$ and $q=-4$.

$$p=2, q=-4$$