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Mathematics Diagnostic Assessment

Use the drawing tool(s) to form the correct answer on the provided graph.

Place a point on the graph to show the location of the [tex]y[/tex]-intercept of the equation given below.

[tex]\[ y = 2^{(4x + 3)} - 1 \][/tex]

\begin{tabular}{|l|}
\hline
Drawing Tools \\
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Select \\
\hline
Point \\
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\end{tabular}

Click on a tool to begin drawing.

Delete



Answer :

To find the [tex]$y$[/tex]-intercept of the equation [tex]\( y = 2^{(4x + 3)} - 1 \)[/tex], we need to determine the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is equal to 0.

Given the equation:
[tex]\[ y = 2^{(4x + 3)} - 1 \][/tex]

Step-by-step solution:

1. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = 2^{(4 \cdot 0 + 3)} - 1 \][/tex]

2. Simplify inside the exponent:
[tex]\[ y = 2^3 - 1 \][/tex]

3. Calculate the power:
[tex]\[ 2^3 = 8 \][/tex]

4. Subtract 1:
[tex]\[ y = 8 - 1 \][/tex]
[tex]\[ y = 7 \][/tex]

So, the [tex]$y$[/tex]-intercept of the equation [tex]\( y = 2^{(4x + 3)} - 1 \)[/tex] is [tex]\( 7 \)[/tex].

Therefore, on the provided graph, you should place a point at [tex]\((0, 7)\)[/tex]. This is the location of the [tex]$y$[/tex]-intercept.