Question

4.

Answer 1

For the first point, remember this simple rule: every exponential function $a^x$ always returns $a$ when evaluated at $x = 1$. In fact, $a^1=a$ for every possible base $a$.

So, we can see that the graph of the exponential passes through the point $(1,y)$ where $y$ appears to be between 1 and 2. So, the only feasible option would be $y = 1.8^x$, because it passes throught the point $(1,1.8)$ because $f(1) = 1.8^1 = 1.8$.

The other functions are wrong because:

• $0.45^x$ would pass through $(1,0.45)$, which would be between 0 and 1 on the y axis
• $2.4^x$ would pass through $(1,2.4)$, which would be between 2 and 3 on the y axis
• $0.31^x$ would pass through $(1,0.31)$, which would be between 0 and 1 on the y axis

As for the second question, you simply have to plug in the values: the function

$f(x) = 7^x$

means that you have to choose an input, x, and use it as exponent for 7. So, if you choose x=2, it means that you have to give exponent 2 to 7, i.e. you replace the x with the specific value, 2.

So, the expression becomes

$f(2) = 7^2 = 49$