Question

evaluate the function for the given value of x.
#1 $y = 2(4)^x$
$x = -2$
#2 $y = -3(5)^x$
$x = 3$
#3 $y = -4(\frac{1}{2})^x$
$x = 2$

#4 if $f(x) = 7(2)^x$ then find the value of $f(0)$
#5 if $f(x) = -3(4)^x$ find the value of $f(1)$

#6 if $f(x) = 8(0.5)^x$ find the value of $f(2)$
#7 find $f(3)$ when $f(x) = \frac{1}{4}(8)^x$

graph of $h(x)$ with x-axis from -5 to 5 and y-axis from 1 to 8
#8 use the function on the graph to find $f(2)$.
#9 find $x$ when $f(x) = 5$

graph of a function with x-axis from -5 to 5 and y-axis from -2 to 8
#10 use the function on the graph to find $f(0)$.
#11 find $x$ when $f(x) = 1$

Explanation:

Let's solve problem #4: If \( f(x) = 7(2)^x \) then find the value of \( f(0) \)

Step 1: Substitute \( x = 0 \) into the function

We have the function \( f(x)=7(2)^x \). To find \( f(0) \), we replace \( x \) with \( 0 \) in the function. So we get \( f(0)=7(2)^0 \)

Step 2: Evaluate \( 2^0 \)

Recall the exponent rule that any non - zero number to the power of \( 0 \) is \( 1 \). So \( 2^0 = 1 \)

Step 3: Calculate the final value

Now we substitute \( 2^0=1 \) back into the expression for \( f(0) \). We have \( f(0)=7\times1 = 7 \)

Answer:

\( 7 \)