Question

Exponential functions: y=-2^x+3 finding the domain, range, and intercepts

Answer 1

domain is all real number because you can raise 2 to any power you like

Answer 2

\[f(x)=-2^x+3\]
range will be \[(-\infty,0)\]

Answer 3

but
\[2^x\geq 0 \] for all x so
\[-2^x\leq 0\] and therefore
\[-2^x+3\leq 3\] for any x

Answer 4

oooops

Answer 5

lol

Answer 6

LOL

Answer 7

I am rusty

Answer 8

agree; totally.

Answer 9

now for intercepts. y intercept put
\[x=0\] get
\[-2^0+3=-1+3=2\] so (0,2) is y intercept

Answer 10

Range is all y values strictly less than 3. There is an horizontal symptom at y=3.

Answer 11

for x intercept set
\[-2^x+3=0\] and solve
you get
\[2^x=3\] so
\[x=\log_3(2)=\frac{\ln(3)}{\ln(2)}\]

Answer 12

last one in case you need a decimal you can use that and a calculator to find it

Answer 13

how would you solve sin^2 (pi/4) - cos^2 (pi/3)

Answer 14

Thank you so much I was basically there but needed to finish it up.

Answer 15

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Answer 16

can someone help me PLEASE?